1. A student took five papers in an examination, where the full marks were the same for each paper. His marks in these papers were in the proportion of 6 : 7 : 8 : 9 : 10. In all papers together, the candidate obtained 60% of the total marks. Then, the number of papers in which he got more than 50% marks is
(a) 1
(b) 3
(c) 4
(d) 5
2. A college has raised 75% of the amount it needs for a new building by receiving an average donation of Rs. 600 from the people already solicited. The people already solicited represent 60% of the people, the college will ask for donations. If the college is to raise exactly the amount needed for the new building, what should be the average donation from the remaining people to be solicited?
(a) 300
(b) 250
(c) 400
(d) 500
3. Forty percent of the employees of a certain company are men and 75% of the men earn more than Rs 25,000 per year. If 45% of the company's employees earn more than Rs 25,000 per year, what fraction of the women employed by the company earn Rs 25,000 per year ?
(a) 2/11
(b) 1/4
(c) 1/3
(d) 3/4
4. In a survey of political preferences, 78% of those asked were in favour of at least one of the proposals : I, II and III, 50% of those asked favoured proposal I, 30% favoured proposal II and 20% favoured proposal III. If 5% of those asked favoured all three of the proposals, what percentage of those asked favoured more than one of the three proposals ?
(a) 10
(b) 12
(c) 17
(d) 22
5. One bacteria splits into eight bacteria of the next generation. But due to environment, only 50% of one generation can produce the next generation. If the seventh generation number is 4096 million, what is the number in first generation ?
(a) 1 million
(b) 2 million
(c) 4 million
(d) 8 million
6. I bought 5 pens, 7 pencils and 4 erasers. Rajan bought 6 pens, 8 erasers and 14 pencils for an amount which was half more what I had paid. What per cent of the total amount paid by me was paid for the pens ?
(a) 37. 5%
(b) 62.5%
(c) 50%
(d) None of these
7. A man earns x% on the first Rs 2,000 and y % on the rest of his income. If he earns Rs 700 from Rs 4,000 and Rs 900 from Rs 5,000 of income, find x%.
(a) 20%
(b) 15%
(c) 25%
(d) None of these
8. The price of a Maruti car rises by 30% while the sales of the car comes down by 20%. What is the percentage change in the Total revenue ?
(a) - 4%
(b) - 2%
(c) + 4%
(d) + 2%
9. A person who has a certain amount with him goes to market. He can buy 50 oranges or 40 mangoes. He retains 10% of the amount for taxi fares and buys 20 mangoes and of the balance, he purchases oranges. Number of oranges he can purchase is
(a) 36
(b) 40
(c) 15
(d) 20
10. 2/5 of the voters promise to vote for P and the rest promised to vote for Q. Of these, on the last day 15% of the voters went back their promise to vote for P and 25% of voters went back of their promise to vote for Q, and P lost by 2 votes. Then, the total number of voters is
(a) 100
(b) 110
(c) 90
(d) 95
Solutions :
1. (c); Let the marks scored in five subjects be 6x, 7x, 8x, 9x and 10x
Total marks in all the five subjects=40x
Max marks of the five subjects=40x/0.6
(∵ 40x is 60% of total marks)
∴ Max marks in each subject=40x/(0.6×5)=13.3 x
Hence, percentage in each subject=6x/13.33x×100, 7x/13.33×100,8x/13.33x×100,(9x×100)/13.33x and (10x×100)/13.33x
Or 45.01%, 52.51%, 60.01%, 67.51% and 75.01%.
∴ Number of papers in which he got more than 50% marks is 4.
2. (a); Let x be the number of people who were asked for donation.
People already solicited=0.6 x,
Remaining people=0.4 x
Amount collected from the people solicited =600×0.6 x=360 x which is 75% of the amount to be collected. Remaining amount 25%=120 x.
∴ Average donation from remaining people=120x/0.4x=300
3. (d); Let number of man and women by 40 and 60 respectively.
∴ Number of men earning more than Rs. 25,000=30
Total number of employees earning more then Rs. 25,000=45
∴ Number of women earning more than Rs. 25,000=(45-30)=Rs. 15
Now, fraction of the women earning Rs. 25,000 or less=(60-15)/60=45/60=3/4
4. (c); Given,
45-(x+y)+25-(x+z)+15-(y+z)+(x+y+z+5)=78
⇒(x+y+z)=12
∴ Percentage of those asked favoured more than one proposal=12+5=17
5. (a); Let number of bacteria in the first generation be x.
∴ Number of bacteria in the second, third, fourth ……………generation would be
8(x/2),8(4x/2),8(16x/2)…………and so on.
x,4x,16x,64x,…..it is a GP with common difference 4. Hence, seventh term of GP=x(4)^6=4096⇒x〖 (2)〗^12=4096
x=1 or 1 million
6. (b); Let 5P+7P_C+4E_R=100………..(i)
∴6P+14P_C+8E_R=150 …………………..(ii)
Multiplying Eq. (i) by 2, we get
10P+14P_C+8E_R=200 ………….(iii)
Solving Eqs. (ii) and (iii) simultaneously, we get
P=12.5.
Hence, total amount paid for 5P=12.5×5=62.5
and it is the required percentage.
7. (b); 2*x/100+2,000*y/100=700 …………..(i)
And 2,000*x/100+3,000*y/100=900………….(ii)
On simplifying these equations change to x+y=35 and 2x+3y=90. Solving these two equations simultaneously we get x=15%
8. (c); Let the original price and sale be 10 unit each. Then, original revenue collection=10×10=100
New price=10×1.3=13, New sale=10×0.8=8
New revenue collection=104.
Hence, revenue is increased by 4%.
9. (d); Suppose the person has Rs. 100 with him.
∴ Price per orange is Rs. 2 and that of a mango is Rs. 2.50. After keeping Rs. 10 for taxi, he is left with Rs. 90.
Price of 20 mangoes=Rs. 40. Remaining money =(90-40)=Rs. 50
So, he can buy50/2.5=20 oranges for this amount.
10. (a); Let total number of votes polled by 100, then votes polled in favour of P=40-6+15=49
Votes polled in favour of Q=60-15+6=51
Difference=51-49=2. It is already given that P lost by 2 votes, hence total number of votes polled=100.
