Q1. Half the girls and one-third of the boys of a college reside in the hostel. What fractional part of the student body is hostel dwellers if the total number of girls in the college is 100 and is one-fourth of the total strength?
(a) Two-fifths
(b) Five-twelfths
(c) One-fifth
(d) Three-eights
(e) None of these
Q2. The monthly incomes of two persons are in the ratio of 4 : 5 and their monthly expenditures are in the ratio of 7 : 9. If each saves Rs. 50 a month, then what are their monthly incomes?
(a) Rs. 100, Rs. 125
(b) Rs. 200, Rs. 250
(c) Rs. 300, Rs. 375
(d) Rs. 400, Rs. 500
(e) None of these
Q3. When a bus started from the first stop, the number of male passengers to the number of female passengers was 3 : 1. At the second stop, 16 passengers got down and 6 more female passengers got in. The ratio of the male to female passengers now become 2 :1. What was the total number of passengers in the bus when it started from the first stop?
(a) 64
(b) 48
(c) 54
(d) 72
(e) 80
Q4. X’s income is three-fourths of Y’s income, and X’s expenditure is fourth-fifths of Y’s expenditure. If X’s income is nine-tenths of Y’s expenditure, find the ratio of X’s savings to Y’s savings.
(a) 1 : 2
(b) 2 : 1
(c) 1 :4
(d) 2 : 3
(e) None of these
Q5. Two persons are climbing up on two moving escalators which have 120 steps. The ratio of 1st person’s speed to that of 1st escalator is 2 : 3 (steps). The ratio of 2nd person’s speed of that of 2nd escalator is 3 : 5 (steps). Find the total number of steps they both have taken together.
(a) 85
(b) 93
(c) 80
(d) 75
(e) None of these
Q6. A man ordered 4 pairs of black socks and some pairs of brown socks. The price of a black pair is double that a brown pair. While preparing the bill, the clerk interchanged the number of black and brown pairs by mistake which increased the bill by 50 per cent. The ratio of the number of black and brown pairs of socks in the original order was:
(a) 4 : 1
(b) 2 : 1
(c) 1 : 4
(d) 1 : 2
(e) None of these
Q7. Two companies A and B quote for a tender. On the tender opening day, A realizes that the two quotes are in the ratio 7 : 4 and hence decreases it price during negotiations to make it Rs. 1 lakh lower than B’s quoted price. B then realises that the final quotes of the two were in the ratio 3 :4. By how much did A decrease its price in order to win the bid?
(a) Rs. 7 lakhs
(b) Rs. 4 lakhs
(c) Rs. 9 lakhs
(d) Rs. 8 lakhs
(e) None of these
Q8. A student is studying for a test from 11:00 am to 8:00 pm on weekdays and one-third of that on Saturdays. On Sundays he takes a break from school and goes fishing. For what fractional part of the entire week is the student studying?
(a) 2/5
(b) 3/7
(c) 2/7
(d) 3/8
(e) None of these
Q9. A sum of Rs. 430 has been distributed among 45 people consisting of men, women and children. The total amounts given to men, women and children are in the ratio 12 : 15 :16. But, the amounts received by each man, woman and child are in the ratio 6 : 5 : 4. Find, what each man, woman and child receives (in Rs.).
(a) 12, 10, 8
(b) 180, 150, 120
(c) 120, 150,160
(d) 60, 75, 80
(e) None of these
Q10. The ratio between the number of passengers travelling by I and II class between the two railway stations is 1 : 50, whereas the ratio of I and II class fares between the same stations is 3 : 1. If on a particular day, Rs. 1325 were collected from the passengers travelling between these stations, then what was the amount collected from the II class passengers?
(a) Rs. 750
(b) Rs. 850
(c) Rs. 1000
(d) Rs. 1250
(e) None of these
Q11. Fresh grapes contain 90 per cent water by weight while dried grapes contain 20 per cent water by weight. What is the weight of dry grapes available from 20 kg of fresh grapes?
(a) 2 kg
(b) 2.4 kg
(c) 2.5 kg
(d) 3 kg
(e) None of these
Q12. In a certain company, the ratio of the number of managers to the number of production-line workers is 5 to 72. If 8 additional production-line workers were to be hired, the ratio of the number of managers to the production-line workers would be 5 to 74. How many managers does the company have?
(a) 10
(b) 20
(c) 30
(d) 25
(e) None of these
Q13. Mayank, Mirza, Little and Jaspal bought a motorbike for Rs. 60,000. Mayank paid one half of the sum of the amounts paid by the other boys, Mirza paid one third of the sum of the amounts paid by the other boys, Little paid one fourth of the sum of the amounts paid by the other boys. How much did Jaspal has to pay?
(a) Rs. 15,000
(b) Rs. 13,000
(c) Rs. 17,000
(d) Rs. 16,000
(e) None of these
Q14. I have one rupee coins, fifty paise coins and twenty five paise coins. The number of coins is in the ratio 2.5 : 3 : 4. If the total amount with me is Rs. 210, find the number of one rupee coins.
(a) 90
(b) 85
(c) 100
(d) 105
(e) None of these
Q15. The cost of diamond varies directly as the square of its weight. Once, this diamond broke into four pieces with weights in the ratio 1 : 2 : 3 : 4. When the pieces were sold, the merchant got Rs. 70,000 less. Find the original price of the diamond.
(a) Rs 1.4 lakhs
(b) Rs 2 lakhs
(c) Rs. 1 lakhs
(d) Rs. 2.1 lakhs
(e) None of these
Solutions
S1. Ans.(d)
Sol. Number of girls = 100
∴ Number of boys = 300
∴ Number of hostel dwellers = 50 + 100 = 150
⇒ Required ratio = 150 : 400
=3∶8=3/8
S2. Ans.(d)
Sol. Let the incomes of the two persons be 4I and 5I respectively
Let the expenditure of the two persons be 7E and 9E respectively.
∴ 4I - 7E = 50 and 5I - 9E = 50
⇒ 20I - 35E = 250
20I - 36E = 200
E = 50 and I = 100
∴ Monthly incomes of the two persons are Rs.400 and Rs. 500 respectively.
S3. Ans.(a)
Sol. Let, initially, the number of males and females in the bus be 3x and x respectively.
At the first stop, suppose m males and f females left the bus.
∴ At the first stop: Number of the males is 3x - m
And number of females
∴ f = 4, x = 16
∴ Total number of passengers in the beginning
= 4x = 64
For no other value of f any of the other alternatives holds good.
S4. Ans.(a)
Sol. Let X’s income be 3k then Y’s income is 4k. Let X’s expenditure be 4g then Y’s expenditure is 5g.
S6. Ans.(c)
Sol. Let x pairs brown socks were ordered
Let p be the price of a brown pair
∴ 2p is the price of a black pair
∴ (2p × 4 + px) + 50% of (2p × 4 + px)
= 2p × x + 4p
⇒ x = 16
∴ Required ratio = 1 : 4
S7. Ans.(b)
Sol. Let the quotes of A and B be 7X and 4X, respectively.
After decreasing, quotes of A = 4x - 1
Then, we are given
⇒ X = 1
Then, decreasing by A = 7X - (4X - 1)
= 3x + 1 = 3 + 1
= Rs. 4 lakhs
S8. Ans.(c)
Sol. Student studies for 9 hrs from 11 am to 8 pm on Monday to Friday
Also, be studies 1/3rd of the time on Sunday i.e. 1/3×9=3h
Total hours, he studied during the week
= 5 × 9 + 3 = 45 + 3 = 48h
Total hours, in a week = 24 × 7 = 168
∴ Required fraction
=48/168=2/7
S9. Ans.(a)
Sol. Ratio of personal shares = 6 : 5 : 4
Ratio of the amounts = 12 : 15 : 16
Ratio of men, women and children
=12/6 ∶15/5 ∶16/4
= 2 : 3 : 4
Sum of these ratios = (2 + 3 + 4) = 9
Number of men =((45 × 2)/9)=10
Number of women =((49 × 3)/9)=15
And, the number of children = 45 - (10 + 15) = 20
Now, dividing Rs. 430 in the ratio = 12 : 15 : 16
Total amount of men’s share
= Rs. ((430 × 12)/43)
= Rs. 120
Total amount of women’s share
= Rs. ((430 × 15)/43)
= Rs. 150
Total amount of children’s share
= Rs. [430 - (120 + 150)]
= Rs. 160
∴ Each man’s share = Rs. (120/10)=Rs.12
Each woman’s share = Rs. (150/15)= Rs. 10
Each child’s share = Rs. (160/20) = Rs. 8
S10. Ans.(d)
Sol. Ratio of the amount collected from the 1st class and the 2nd class passengers = 3 : 50
∴ Amount collected from the 2nd class passengers
=50/53×1325 = Rs. 1250.
S12. Ans.(b)
Sol. According to question,
5x/(72x + 8)=5/74
⇒ x = 4
Managers = 5 × 4 = 20
S13. Ans.(b)
Sol. Mayank paid 1/2 of the sum paid by other three.
Let the other three paid Rs. x jointly, then Mayank paid x/2
Let the other three paid Rs. x jointly, then Mayank paid x/2
So, x+x/2=60,000 ⇒ x = 40,000.
Hence, Mayank paid = Rs. 20,000
Likewise, Mirza and Little paid Rs. 15,000 and Rs. 12,000 respectively.
Hence, the amount paid by Jaspal is
Rs. [60,000 - (20,000 + 15,000 + 12,000)] = Rs. 13,000
Rs. [60,000 - (20,000 + 15,000 + 12,000)] = Rs. 13,000
S14. Ans.(d)
Sol. Ratio of number of one rupee, fifty paise, and twenty five paise coins = 2.5 : 3:4
∴ Ratio of value of coins =2.5×1∶3/2 ∶4/4=5∶3∶2
Let, amount of Rs 1, 50 paise and 25 paise coins be 5x, 3x and 2x respectively.
So, 5x + 3x + 2x = 210 (given) ⇒ x = 21
∴ Value of one rupee coins
= number of one rupee coins = 21 × 5 = 105
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