Daily GK Update 09th August 2017

1. Justice Dipak Misra to be next Chief Justice of India

i. The Union government appointed Justice Dipak Misra as the next Chief Justice of India. He will be replacing incumbent Justice J S Khehar, who is set to retire on August 27, 2017.

ii. It was Khehar who had recommended Misra's name to succeed him as the next Chief Justice of India. Justice Misra will be sworn in as the 45th Chief Justice of India by President Ram Nath Kovind on August 27. Justice Misra will retire on October 2, 2018.

Important Takeaways from Above News-

• Justice H.J Kania was the first Chief Justice of India.

2. Nagasaki Day: 9th August

i. The atomic age began with the US dropping the first atomic bomb dubbed “Little Boy” on August 6, 1945, on the Japanese city of Hiroshima, after its July 16 pre-dawn birth in successful testing at Alamogordo, New Mexico.

ii. Three days later, on August 9, 1945, the second bomb—“Fat Man”—was dropped on Nagasaki, incinerating the city and its unexpecting inhabitants. Their combined devastation was unimaginable.

Important Takeaways from Above News-

• Sparked by Adolf Hitler in 1939, the world war II started in 1939 and ended in 1945.

3. Nation celebrates 75th anniversary of Quit India Movement

i. India has celebrated the 75th anniversary of the Quit India Movement. This year’s theme is “SANKALP SE SIDDHI"- the Attainment through Resolve. Prime Minister Narendra Modi in his recent Mann Ki Baat program had called for launching the mega campaign Sankalp Se Siddhi.
ii. The exhibition has been organized titled “Quit India-75-Chalo Dilli” and it will be thrown open to public after inauguration till 1st of September.

Important Takeaways from Above News-

• The Quit India Movement was an important milestone in the Indian freedom struggle. Under the leadership of Mahatma Gandhi, people across India came together to uproot imperialism.

4. Sri Lankan Navy commissions India-built AOPV

i. Sri Lankan Navy has commissioned an India-built state-of-the-art Advanced Offshore Patrol Vessel (AOPV), the first-ever purchase from a foreign ship builder, to boost its search and rescue capabilities.

ii. Sri Lankan President and Armed Forces commander-in-chief Maithripala Sirisena commissioned the new patrol vessel “SLNS Sayurala”. It is the largest vessel built by an Indian ship builder for a foreign navy to date. Built at the Goa Shipyard Ltd (GSL) in India, SLNS Sayurala is the first-ever brand new platform purchased from a foreign ship builder.

Important Takeaways from Above News-

• Ranil Wickremesinghe is the PM of Sri Lanka.
• Sri Jayewardenepura Kotte is the official capital of Sri Lanka.

5. Coconut regains 'tree' status in Goa as Assembly passes bill

i. The Goa Legislative Assembly passed a bill which reclassifies coconut as a `tree', ensuring legal protection for it. Goa Forward Party, a partner in the Manohar Parrikar-led government, had promised to reclassify coconut.

ii. The previous Laxmikant Parsekar-led government had changed classification of coconut tree to a `palm'. The Assembly, on the last day of Monsoon session, passed the Goa, Daman and Diu (Preservation of) Trees Act, 1984 to regulate felling of coconut trees and reclassify it as a tree.

Important Takeaways from Above News-

• Current Chief Minister of Goa is Manohar Parrikar.
• Smt. Mridula Sinha is the Governor of Goa.

6. 8th meeting of Regional Technical Group on Trade, Commerce and Investment CBM of the Heart of Asia – Istanbul Process held in New Delhi

i. The eighth meeting of the Regional Technical Group of Confidence Building Measure on Trade, Commerce & Investment Opportunities under the Heart of Asia – Istanbul Process was hosted by India in New Delhi.
ii. The meeting was co-chaired by the Acting Director General, Economic Cooperation Department, Ministry of Foreign Affairs of Afghanistan, Mr. Hassan Soroosh, and Joint Secretary, Ministry of External Affairs, Dr. Deepak Mittal and attended by representatives of 17 participating countries and supporting international organisations, including Azerbaijan, Iran, Kyrgyzstan, Pakistan, Russia, Tajikistan, Turkey, Turkmenistan, UAE, Australia, Egypt, Germany, the UK, the US, the EU and the UN.

Important Takeaways from Above News-

• Istanbul is a major city in Turkey. 
• Kabul is the Capital of Afghanistan.

7. Bajaj Ties Up With Triumph to Make Mid-Capacity Motorcycles

i. Bajaj Auto and Triumph Motorcycles UK have announced a global partnership. This non-equity tie-up between Bajaj and Triumph will enable the former to build a range of mid-capacity motorcycles, building on the collective strengths of both companies.

ii. The aim of this partnership is to deliver a range of outstanding mid-capacity motorcycles. It will enable to offer a wide range of motorcycles within its domestic market and other international markets.

Important Takeaways from Above News-

• Shri Kamalnayan Bajaj was the founder of Bajaj Auto.
• Rahul Bajaj is the Chairman of Bajaj Auto.

8. Dev Patel to be honored with Asia Society Game Changers Award

i. Indian-origin actor Dev Patel is to be honored by a leading educational organization for making a “transformative and positive” difference for the future of Asia and the world.

ii. London-born Dev Patel, who became popular with his debut film Slumdog Millionaire, will be felicitated with the Asia Society 2017 Asia Game Changers Award at a ceremony to be held at the United Nations, New York, in November 2017.

Important Takeaways from Above News-

• He was recently seen in Garth Davis’ Lion, which earned him an Academy Award nomination for the best actor in a supporting role.

9. Hrithik Roshan Inks Rs 100 crore Deal with Startup Cure.Fit

i. Hritik Roshan has been signed as a brand ambassador by a health and wellness startup Cure.fit in a deal worth Rs 100 crore. The actor will be associated with the brand for five years.

ii. The deal also includes the actor's equity stake in the company in lieu of cash investment, promotions and royalty from his personal brand HRX's specialised workout plan. Cure.fit will soon be launched as a mobile app and is expected to rake in Rs 250-crore annual business in the coming years.

10. Flipkart Launching 'Budding Star Programme' for Staff 

i. Flipkart has launched 'Budding Star Programme', an exclusive programme aimed at Flipkart employees to help them achieve their dreams by providing them financial assistance and paid leave.

ii. The programme will cover all national and international sports and non-sports competitors recognized by the govt. authorities. Flipsters who have completed six months with the company are eligible for the ‘Budding Star Programme’.

Important Takeaways from above News-

• CEO of flipkart is Kalyan Krishnamurthy.

11. Indian American Appointed US County's Deputy Comptroller For Minority Affairs

i. Indian American Dilip Chauhan has been appointed to a key position of Deputy Comptroller for Minority Affairs in New York's Nassau county.

ii. Chauhan had joined the Comptroller’s office in 2015 as Director for Community Affairs, South and East Asia. He has served as senior advisor to the Comptroller since early 2017.

Important Takeaways from Above News-

• Nassau is the capital city and commercial centre of the Commonwealth of the Bahamas.

12. ICICI Bank launches instant credit cards

i. The country's largest private sector lender, ICICI Bank, launched instant credit cards enabling its savings account customers to get a credit card instantly, in a completely digital and paperless manner.

ii. The bank has opened up this offering to a few lakh of pre-qualified customers who can apply for the card online and generate card details and start shopping online instantly. Currently, this facility to apply for a credit card in–a-flash is available through the Bank’s internet banking platform. It will also be available shortly on iMobile, the Bank’s mobile banking application.

Important Takeaways from Above News-

• CEO of ICICI Bank is Chanda Kochhar.
• Headquarter of ICICI is in Mumbai.

13. IDFC Bank partners with Zeta for digital payments solution

i. Private sector lender IDFC Bank has partnered with digital payments company Zeta, to launch ‘IDFC Bank Benefits’. It is a payment solution for corporates that digitizes employee spends and claims, making the process simple, real-time and paperless.

ii. The end-to-end digital solution comprises an IDFC Bank Benefits Card and Zeta app which integrates the full suite of allowances and reimbursements offered by an employer into one preloaded card. Employees can also access the Benefits Card via the Zeta app on mobile or web. The Zeta app offers employees a real time view of spends, reimbursement limits and claims.

Important Takeaways from Above News-

• Mr. Sunil Kakar is the Managing Director & CEO of IDFC Limited.

14. Syndicate Bank Cuts MCLR by 5-10 bps

i. Syndicate Bank has pared its marginal cost of funds based lending rate (MCLR) by 5-10 basis points in certain maturity buckets.

ii. MCLR for six months and one year will be 8.3 per cent (8.35 per cent now) and 8.5 per cent (8.60 per cent now), respectively, with effect from August 10.

Important Takeaways from Above News-

• Headquarter of Syndicate Bank is in Manipal, Karnataka.

15. Axis Bank Cuts Savings Account Interest Rate by 50 bps

i. Private sector lender Axis Bank reduced interest rate on savings bank accounts by 50 basis points to 3.5 per cent for deposits up to Rs 50 lakh.

ii. However, the bank will continue to pay 4 per cent interest on deposits of above Rs 50 lakh. 

Important Takeaways from Above News-

• Shikha Sharma is the Managing Director & CEO of Axis Bank.

16. Indian-origin entrepreneur named Canada's consul general in San Francisco

i. Rana Sarkar, an Indo-Canadian entrepreneur, has been appointed Canada's consul general in San Francisco as well as a member of the Canadian official team tasked with renegotiating the North American Free Trade Agreement (NAFTA) with the US and Mexico.
ii. Sarkar is part of a 13-member group tasked with helping Canada navigate the renegotiation of NAFTA.

Important Takeaways from Above News-

• From 2009 to 2013, Sarkar was president and CEO of the Canada-India Business Council.
• The capital of Canada is Ottawa.

17. Netflix Made its 'First Ever' Acquisition

i. Online entertainment platform Netflix announced that it has acquired Millarworld, a comic book company.

ii. The acquisition was the first ever by Netflix. Together, the two companies will bring Millarworld's portfolio of character franchises to life through films, series and children's shows available exclusively to Netflix members. Millar developed the comic books and story arcs that inspired the first Avengers movie, “Captain America: Civil War,” and “Logan (Wolverine).

Important Takeaways from Above News-

• Reed Hastings is the co-founder and CEO of Netflix.

Important Tricks and Quiz on Profit and Loss

Important Tricks and Quiz on Profit and Loss

Hello Readers,

Below in the post ,We shall discuss about Profit and Loss of the Quant section.  Now a days these topics  have became an important part of the Quant test ,So Here we will help you in this.We will  provide short tricks and quant quiz.

TRICKS  FOR SOLVING QUESTIONS RELATED TO PROFIT AND LOSS:

COST PRICE : The price at which an article is purchased is called its cost price (C.P.)

SELLING PRICE : The price at which the article is sold is called its selling price (S.P.)

1. If the cost price (C.P.) of the article is equal to the selling price (S.P.), then there is no loss or gain.

2. If the selling price (S.P.) > cost price (C.P.), then the seller is said to have a profit or gain,

Gain/Profit = S.P. - C.P.

3. If the cost price (C.P.) > selling price (S.P.), then the seller is said to have a loss,

Loss = C.P. - S.P.

4.  Gain% = {(Gain*100)/C.P.}

5. Loss% ={(Loss*100)/C.P.}

6. S.P. = {(100+Gain%)/100 * C.P.}

7. S.P. = {(100 - Loss%)/100 * C.P.}

8. C.P. = {(100/(100+Gain%) * S.P.}

9.C.P. = {(100/(100 - Loss%) * S.P.}

10. If an article is sold at a profit/gain of 30%, then S.P. = 130% of the C.P.

11. If an article is sold at a loss of 20%, then S.P. = 80% of the C.P.

12. When a person sells two similar items, one at a gain of say x%, and the other at a loss of x%, then in this transaction the seller always incurs a loss given by: 

                        {x^2/100}%

13. A single discount equivalent to discount series of x% and y% given by the seller is equal to 

                                   {x +y - xy/100}%

14. If a trader professes to sell his goods at cost price, but uses false weights, then 

Gain% = {Error/(True value - Error) x 100}%

 1. How much percent more than the cost price should a shopkeeper mark his goods so that after allowing a discount of 25% on the marked price, he gains 20%?

A.  60%

B.  55%

C.  70%

D.  50%

2. A dishonest dealer professes to sell his goods at the cost price but uses a false weight of 850 g instead of 1 kg. His gain percent is

A.  71 11/17%

B.  11 11/17%

C.  17 12/17%

D.  17 11/17%

3. An article is sold at 10% loss. If the selling price is Rs. 40 more, there will be a gain of 15%. The cost price of the article is:

A.  Rs. 140

B.  Rs. 120

C.  Rs. 175

D.  Rs. 160

4. The cost price of 20 articles is the same as the selling price of x articles. If the profit is 25%, find out the value of x

A. 15

B. 25

C. 18

D. 16

5.In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit?

A. 30%

B. 70%

C. 100%

D. 250%

6.The percentage profit earned by selling an item for Rs. 1920 is equal to the percentage loss incurred by selling the same item for Rs. 1280. At what price should the item be sold to make 25% profit?

A. Insufficient Data

B. Rs. 3000

C. Rs. 2000

D. Rs. 2200

7. Some articles were bought at 6 articles for Rs. 5 and sold at 5 articles for Rs. 6. Gain percent is:

A. 30%

B. 33 1/3%

C. 35%

D. 44%

8. 100 oranges are bought at the rate of Rs. 350 and sold at the rate of Rs. 48 per dozen. The percentage of profit or loss is:

A. 14 2/7% gain

B. 15% gain

C. 14 2/7 % loss

D. 15 % loss

9.A trader mixes 26 kg of rice at Rs. 20 per kg with 30 kg of rice of other variety at Rs. 36 per kg and sells the mixture at Rs. 30 per kg. What is his profit percentage?

A. 6%

B. 5%

C. 4%

D. 7%

10. A trader gives 12% additional discount on the discounted price, after giving an initial discount of 20% on the labeled price of an item. The final sale price of the item is Rs.704. Find out the labeled price?

A. 1000

B. 2000

C. 1200

D. 920

ANSWER AND SOLUTION :

1(A)Explanation :
Let cost price of goods be Rs 100.
Gain = 20%
Therefore, Selling price = Rs 120
Discount = 25%
Marked Price = (100/100-25)x120
= Rs. 160
i .e.  60% more

2(D)Explanation :
If a trader professes to sell his goods at cost price, but uses false weights, then
Gain% = {Error/(True value - Error) x 100}%
In the given question, Error = 1000 - 850 = 150
Thus, Gain% = {150/(1000 - 150) x 100}%
= 17 11/17%

3(D)Explanation :
Let the cost price be Rs. x.
Selling Price at 10% loss = 90x/100
Selling Price at 15% gain = 115x/100
Thus, according to the problem,
115x/100 - 90x/100 = 40
x = Rs.160

4(D)Explanation :
Let the Cost Price (CP) of one article = 1
=> CP of x articles = x ------------------------------(Equation 1)
CP of 20 articles = 20
Given that cost price of 20 articles is the same as the selling price of x articles
=> Selling price (SP) of x articles = 20--------------(Equation 2)
Given that Profit = 25%
(SP-CP/CP)=25/100=1/4------------( Equation 3)
Substituting equations 1 and 2 in equation 3,
(20-x)/x=1/4
80-4x=x
5x=80
x=80/5=16

5(B)Explanation:
 Let C.P.= Rs. 100. Then, Profit = Rs. 320, S.P. = Rs. 420.
New C.P. = 125% of Rs. 100 = Rs. 125
New S.P. = Rs. 420.
Profit = Rs. (420 - 125) = Rs. 295.
 Required percentage = (295/420 x 100)% = 1475/21 % = 70% (approximately).

6(C)Explanation :
Let CP = x
Percentage profit earned by selling an item for Rs. 1920
= (SP-CP/CP0 ×100
=(1920-x)/x×100
Percentage loss incurred by selling the same item for Rs. 1280
= (CP-SP)/CP×100
= (x-1280)/x ×100
Given that Percentage profit earned by selling an item for Rs. 1920=Percentage loss incurred by selling the same item for Rs. 1280
(1920-x)/x ×100 = x-1280/x ×100
(1920-x)/x = (x-1280)/x
1920–x = x–1280
2x=1920+1280=3200
x=3200/2
=1600
Required Selling Price = CP×125/100
=1600×125/100 =1600×5/4
=400×5=2000

7(D)Explanation:
Suppose, number of articles bought = L.C.M. of 6 and 5 = 30.
C.P. of 30 articles = Rs.(5/6 x 30) = Rs. 25.
S.P. of 30 articles = Rs.(6/5 x 30) = Rs. 36.
 Gain % =  (11/25 x 100) % = 44%.

8(A)Explanation:
C.P. of 1 orange = Rs.(350/100) = Rs. 3.50
S.P. of 1 orange = Rs (48/12) = Rs. 4
 Gain% = (0.50/3.50  x 100) %  = 100/7 % = 14 2/7%

9(B)Explanation :
CP of 1st variety rice=20
CP of 2nd variety rice=36
CP of the 56 kg rice mixture=(26×20+30×36)=520+1080=1600
SP of the 1 kg rice mixture=30
SP of the 56 kg rice mixture=30×56=1680
Gain=SP-CP=1680-1600=80
Gain%=Gain/CP×100=80/1600×100=100/20=5%

10(A)Explanation :
Let the labeled price=x
SP=704
Initial Discount=20%
Price after initial discount=x×80/100
Additional discount=12%
Price after additional discount=x×80/100 × 88/100
But Price after additional discount=SP=704
=> x×80/100 × 88100=704
=>x×4/5 × 22/25=704
=>x=704×25/22 × 5/4=176×25/22×5
=8×25×5=40×25=1000

Tricks and concepts on Profit and Loss

Concept And Tricks On Average

Concept And Tricks On Average

What is Average

An average or more accurately an arithmetic mean is, in crude terms, the sum of n different data divided by n.

Averages of a group is defined as the ratio of sum of all the items in the group to the number of items in the group.

Average = (Sum of all items in the group)/ Number of items in the group

Now, sum of all items can be ‘the sum of number of quantities like apple, people etc’ or ‘sum of values of the item like 10 coins of 2Rs each etc’.

Some Important Concepts:

1. Average =total of data/No.of data

2. If the value of each item is increase by the same value a, then the average of the group or items will also increase by a.

3. If the value of each item is decreased by the same value a, then the average of the group of items will also decrease by a.

4. If the value of each item is multiplied by the same value a, then the average of the group or items will also get multiplied by a.

5. If the value of each item is multiplied by the same value a, then the average of the group or items will also get divided by a.

6. If we know only the average of the two groups individually, we cannot find out the average of the combined group of items.

7.Average of n natural no's=(n+1)/2

8.Average of even No'=(n+1)

9.Average of odd No'= n

10.General Formula=(1st number +Last number)/2

SSC CGL 2017 Tier-I

SSC CGL 2017 Tier-I third shift is over. These questions are based on the type of GA questions asked in the THIRD Shift of the exam (9th August). Candidates having CGL Exam in other shifts can go through these questions and can expect these questions to be asked in upcoming shifts as well.

Q1.Ozone is an_____ of oxygen ?
Ans:Allotropes

Q2.Which of the following is inert gas? 

Q3.Anti-defection law comes in which schedule?
Ans:10th schedule 

Q4. Second Battle of Tarain was fought between?
Ans:Prithviraj Chauhan was defeated by Mohammed Ghori.

Q5.Who is the inventor of frozen food? 
Ans:Clarence Birdseye 

Q6.What is the full form of M-SIP ?
Ans:Modified Special Incentive Package Scheme

Q7.Who regulates Rural Regional Bank? 

Ans:NABARD

Q8.Recently which country test fired surveillance missile against North Korea?

Q9.Who got Padma Shri for cooking in 2017?
Ans:Sanjeev Kapoor

Q10.Match the following

Berdi-tennis

Hit wicket- cricket

Volley-tennis

Q11.Who is the founder of Banaras Hindu University? 
Ans:Madan Mohan Malaviya

Q12.When was 'Dal badal Sanshodhan' implemented? 
Ans:52nd Amendment, 1985

Q13.Who is the author of the book "Out of my Window"?

Ans:Gail Albert Halaban

Q14.Who is the head of defence?

Q15. Jhulta Minar is located in which City? 

Ans:Ahmedabad

Q16.What is the SI unit of frequency?
Ans:hertz

Q17.Convex mirror are used in ?
Ans: rear view mirror

Q18.Polio and chickenpox are caused by virus/bacteria?
Ans:Virus

Q19.Which of the following metal is abundant in the earth?
Ans:Aluminium

Q20. Red Data Book consists of which of the following?
Ans:Endangered Species

Q21. One question was asked from soil?

Q22. Tawang dispute was held in between whom?
Ans: China and India

Q23. Which of the following is the "Modifier key"?
(a) Ctrl
(b) Shift
(c) Alt
(d) All of the above
Ans. (d) All of the above

SSC CGL 2017 Tier-I

SSC CGL 2017 Tier-I first shift is over. These questions are based on the type of GA questions asked in the Second shift of the exam (9th August). Candidates having CGL Exam in other shifts can go through these questions and can expect these questions to be asked in upcoming shifts as well.

Q1-Amazon river flows through which country?
Ans:South America

Q2-Konark temple was made by which king?
Ans:Narasimhadeva I

Q3-India shares maximum borderline with which country?
Ans:Bangladesh

Q4-Forest Research Institute of India is in which state?
Ans: Dehradun in Uttarakhand

Q5-Similar types of cells form?

Q6-Question related to Types of plant tissues.

Q7- Who is the Author of the book 'Numbers do lie'?
Ans:Aakash Chopra

Q8-Who is the Executive head of INDIA?

Q9-What Constitutes the Parliament?

Q10-Din Dayal Scheme is implemented in which state?

Q11-First Governor General of Bengal?

Q12-Property of electromagnetic waves?

Q13-Miss Universe 2016

Q14-UN Secretary General

Q15-Who discovered bacteria?

Q16-Disguised unemployment meaning?

Q17. Which state has Longest Coastline ?

SSC CGL 2017 Tier-I

SSC CGL 2017 Tier-I first shift is over. These questions are based on the type of GA questions asked in the first shift of the exam (9th August). Candidates having CGL Exam in other shifts can go through these questions and can expect these questions to be asked in upcoming shifts as well.

Q1. How many players are in Volleyball team?
Ans:Six

Q2. What is the reason of mirage formation?
Ans:Total Internal Reflection

Q3.Why is the bending of light in slit?

Q4. Which of the following is not a member of BRICS ?
Ans:The Members of BRICS are :Brazil, Russia, India, China and South Africa.


Q5. Kalapani is a disputed territory between India and which country?
Ans:Nepal

Q6. What is Ujjawala Scheme?
Ans:Provides free LPG connections to the women below BPL.

Q7.Which type of blood cell is responsible for the transportation of oxygen ?
Ans:RBC

Q8.Who won the 2016 Global Indian of the Year award?
Ans:Aishwarya Rai Bachchan

Q9. Which removes wastes and extra water from the blood to form urine?
Ans:Kidney

Q10.Who gives oath to the President of India?
Ans:Chief Justice of India

Q11.Tropical Cyclone in china is known by the name?
Ans:Typhoon

Q12. acid + base → ---- + water
Ans:Salt

Q13. Sovereignty in Constitution related question.

Q14.Who gave theory of equilibrium in economics?
Ans:Leon Walras

Q15. Match of the following: Temples and State ?

Q16.Book Author related question.

Q17. Who invented television?

Q18. Mahatma Gandhi’s first Satyagraha movement?

Ans:The Champaran Satyagraha of 1917

Mixture and Alligation

Important Concepts and Formulas - Mixture and Alligation1. AlligationAlligation is the rule which enables us to find the ratio in which two or more ingredients at the given price must be mixed to produce a mixture of a specified price.
2. Mean PriceMean price is the cost price of a unit quantity of the mixture

3. Suppose a container contains $x$ units of a liquid from which $y$ units are taken out and replaced by water. After $n$ operations, quantity of pure liquid
$=x{(1-\frac{y}{x})}^n$ units.

4. Rule of AlligationIf two ingredients are mixed, then
$\left(\frac{\text{Quantity of cheaper}}{\text{Quantity of dearer}}\right)$ $=\left(\frac{\text{CP of dearer - Mean Price}}{\text{Mean price - CP of cheaper}}\right)$

The above formula can be represented with the help of the following diagram which is easier to understand.


=> (Cheaper quantity) : (Dearer quantity) = (d - m) : (m - c)

Proof of Rule of Alligation formula

Let cost price of unit quantity of cheaper ingredient = c
cost price of unit quantity of dearer ingredient = d

Suppose 'a' units of cheaper ingredient and 'b' units of dearer ingredient are mixed.

Total quantity of the mixture = a + b
Total cost price of the mixture = (ac + bd)

cost price of unit quantity of the mixture (mean price) = $\frac{\text{ac + bd}}{\text{a+b}}$

Suppose mean price = m
=> $\frac{\text{ac + bd}}{\text{a+b}}$ = m
=> am + bm = ac + bd
=> am - ac = bd - bm
=> a(m - c) = b(d -m)
=> a/b = (d -m)/(m - c)
=> a : b = (d -m):(m - c)