APTITUDE II

Problems on Numbers

Example

The average of four consecutive even numbers is 27. Find the largest of these numbers.
Sol. Let the four consecutive even numbers be X, X + 2, X +4 & X + 6
Their total sum = (27 × 4) = 108.
X + X +2 +X + 4 + X + 6 = 108 or 4X = 96 or X = 24.
Largest number = (X +6) = 30.

Exercise

1. A number exceeds 20% of itself by 40. The number is
a) 50 b) 60 c) 80 d) 320
Ans: a) 50
2. If 16% of 40% of a number is 8, the number is
a) 320 b) 225 c) 200 d) 125
Ans: d) 125
3. The difference of two numbers is 20% of the larger number. If the smaller number is 12, the larger one is
a) 16 b) 15 c) 18 d) 20
Ans: b) 15
4. I one-seventh of a number exceeds its eleventh part by 100, then the number is
a) 770 b) 1100 c) 1825 d) 1925
Ans: d) 1925
5. The sum of the square of two numbers is 3341 and the difference of their square is 891. The numbers are
a) 25, 46 b) 35, 46 c) 25, 36 d) none of these
Ans: b) 35, 46
6. The numbers which when added to 10 times itself gives 264, is
a) 20 b) 22 c) 24 d) 26
Ans: c) 24
7. A number when divided by 4 is reduced by 21. The number is
a) 18 b) 20 c) 28 d) 38
Ans; c) 28
8. A number exceeds its four-seventh by 18. What is the number ?
a) 36 b) 49 c) 63 d) None
Ans: None
9. The sum of three consecutive odd numbers is 57. The middle one is
a) 17 b) 19 c) 21 d) 23
Ans: b) 19
10. The sum of the digits of a two-digit number is 9 less than the number. Which of the following digits is at unit place of the number?
a) 1 b) 2 c) 4 d) Data inadequate
Ans: d) Data inadequate

Percentage

Example

Which is greatest in 16 2/3%, 2/15 and 0.17 ?
Sol. 16 2/3% = (50/3 × 1/100) = 1/6 = 0.1666,
2/15 = 0.133 & the third number is 0.17.
Clearly, 0.17 is the greatest.

Exercise

1. If 30% of a number is 12.6, then the number is
a) 41 b) 51 c) 52 d) 42
Ans: d) 42
2. If 15% of 40 I greater than 25% of a number by 2, the number is
a) 16 b) 20 c) 24 d) 32
Ans: a) 16
3. What will be 160% of a number whose 200% is 140?
a) 200 b) 160 c) 140 d) 112
Ans: d) 112
4. If 75% of a number is added to 75, the result is the number itself. Then, the number is
a) 400 b) 300 c) 600 d) 50
Ans: b) 300
5. The population of a town has increased from 133575 to 138918. The percent increase in population is
a) 2.5 b) 3 c) 3.5 d) 4
Ans: d) 4
6. Subtracting 6% of x from x is equivalent to multiplying x by how much?
a) .94 b) 9.4 c) .094 d) 94
Ans: .94
7. It is known that 20% of the mangoes are rotten. If the number of rotten mangoes is 35, then the total number of mangoes is
a) 150 b) 175 c) 180 d) 185
Ans: b) 175
8. A student has to secure 40% marks to pass. He gets 178 marks and fails by 22 marks. The maximum marks are
a) 200 b) 500 c) 800 d) 1000
Ans: b) 500
9. A reduction of 12.5% in the price of a dining table brought down its price to Rs. 4375. The original price (in Rs.) of the table was
a) 6000 b) 5400 c) 5200 d) 5000
Ans: d) 5000
10. In an examination, 1100 boys and 900 girls appeared. 50% of the boys and 40% of the girls passed the examination. The percentage of candidates failed is
a) 45 b) 45.5 c) 54.5 d) 59.2
Ans: c) 54.5
11. 300 grams of sugar solution has 40% sugar in it. How much sugar should be added to make it 50 % in the solution?
a) 10 gms b) 40gms c) 60 gms d) 80 gms
Ans: c) 60 gms
12. The price of an article is cut by 20%. To restore it to the former value, the new price must be increased by
a) 20% b) 25% c) 16 d) 24%
Ans: b) 25%
13. A’s income is 25% more than B’s income in terms of A’s income is
A) 75% b) 80% c) 90% d) 96%
Ans: b) 80%
14. The price of sugar is increased by 20%. As a result, a family decreases its consumption by 25%. The expenditure of the family on sugar will be decreased by
a) 10% b) 5% c) 14% d) 15%
Ans: a) 10%
15. The length and breath of a square are increased by 40% and 30% respectively. The area of the resulting rectangle exceeds the area of the square by
a) 42% b) 62% c) 82% d) None
Ans: c) 82%

Problems on Ages

Example

Ramu was 4 times as old as his son 8 years ago. After 8 years, Ramu will be twice as old as his son. What are their present ages?
Sol. Let son’s age 8 years ago be X years.
Then, Ramu’s age at that time = 4X years.
Son’s age after 8 years = (X + 8) + 8 = (X + 16) years.
Ramu’s age after 8 years = (4X + 8) + 8 = (X + 16) years.
2(X + 16) = 4X + 16 or x = 8.
Son’s present age = (X + 8) = 16 years.
Ramu’s present age = 4X + 8) = 40 years.

Exercise

1. The ratio of the ages of Meena and Meera is 4: 3. The sum of their ages is 28 years. The ratio ages after 8 years will be
a) 4: 3 b) 12: 11 c) 7: 4 d) 6: 5
Ans: d) 6: 5
2. The ages of Ram and Mukta are in the ration of 3: 5. After 9 years the ratio of their ages will becomes 3: 4. The present age of Mukta (in years) is
a) 9 b) 15 c) 18 d) 24
Ans: b) 15
3. In 10 years, a will be twice as old as B was 10 years ago. If A is now 9 years older than B, the present age of B is
a) 19 years b) 29 years c) 39 years d) 49 years
Ans: c) 39 years
4. Two years ago a man was 6 times as old as his son. After 18 years he will be twice as old as his son. Their present ages (in years) are
a) 32, 7 b) 34, 9 c) 36, 11 d) None of these
Ans: d) None of these
5. The ages of two persons differ by 20 years. If 5 years ago, the elder one be 5 times as old as the younger one, their present ages (in years) are respectively
a) 30, 10 b) 25, 5 c) 29, 9 d) 50, 30
Ans: b) 25, 5
6. Pushpa is twice as old as Rita was 2 years ago. If the difference of their ages be 2 years, how old is Pushpa today?
a) 6 years b) 8 years c) 10 years d) 12 years
Ans: b) 8 years
7. Ratio of Ashok’s age to Sandeep’s age is 4:3. Ashok will be 26 years old after 6 years. How old is Sandeep now?
a) 12 years b) 15 years c) 19 years d) 21 years
Ans: b) 15 years
8. The ratio of Vimal’s age and Aruna’s age is 3: 5 and the sum of their ages is 80 years. The ratio of their ages after 10 years will be
a) 2: 3 b) 1: 2 c) 3: 2 d) 3: 5
9. The average age of 12 students is 20 years. If the age of one more student is included, the average decreases by 1. What is the age of the new student?
a) 5 years b) 7 years c) 9 years d) 11 years
Ans: b) 7 years
10. The average age of an adult class is 40 years. Twelve new students with an average age of 32 years join the class, thereby decreasing the average of the class by 4 years. The original strength of the class was
a) 10 b) 11 c) 12 d) 15
Ans: c) 12

Profit &Loss

Example

Hari purchased 25 kg of wheat at Rs. 4 per kg and 35 kg of wheat at Rs. 4.50 per kg. he sold the mixture at Rs. 4.25 per kg. Finds his gain or loss.
Sol. Total C.p = Rs. (25 × 4 + 35 × 4.50) = Rs. 257.50.
Total S.P. = Rs. (60 × 4.25) = Rs. 255.
Loss = Rs. (257.50 – 255) = =Rs. 2.50.

Exercise

1.Cost of 3 cricket balls = cost of 2 pairs of leg pads.
Cost of 3 pairs of leg pads = cost of 2 pairs of gloves.
Cost of 3 pairs of gloves = cost of 2 cricket bats.
If a cricket bat costs Rs.54, what is the cost of a cricket ball?
a) Rs.12 b) Rs.14 c) Rs.16 d) Rs.18
Ans: c) Rs.16
2.There would be 10% loss if a toy is sold at Rs. 10.80 per price. At what price should it be sold to earn a profit of 20%?
a) Rs.12 b) Rs.12.96 c) Rs.14.40 d) None
Ans: c) Rs.14.40
3. A fruit seller purchases oranges at the rate of 3 for Rs 5 and sells them at 2 for Rs 4. His profit in the transaction is
a) 10% b) 15% c) 20% d) 25%
Ans: c) 20%
4. A man bought a number of oranges at 3 for a rupee and an equal number at 2 for a rupee. At what price per dozen should he sell them to make a profit of 20%?
a) Rs 4 b) Rs 5 c) Rs 6 d) Rs 7
Ans: c) Rs 6
5. A man buys oranges at Rs 5 a dozen and an equal number at Rs 4 a dozen. He sells them at Rs 5.50 a dozen and makes a profit of Rs 50. How many oranges does he buy ?
a) 30 dozens b) 40 dozens c) 50 dozens d) 60 dozens
Ans: c) 50 dozens
6. By selling 45 lemons for Rs. 40, a man loses 20%. How many should he sell for Rs 24 to gain 20% in the transaction ?
a) 16 b) 18 c) 20 d) 22
Ans: b) 18
7.A person bought 20 litres of milk at the rate of Rs 8 per litre. He got it churned after spending Rs 10 and got 5 kg of gream and 20 litres of toned milk. If he sold the cream at Rs. 30 per kg and toned milk at Rs 4 per litre, his profit in the transaction is
a) 25% b) 35.3% c) 37.5% d) 42.5%
Ans: b) 35.3%
8. A sells a bicycle to B at a profit of 20% and B sells it to C at a profit of 25%. If C pays Rs 1500, what did A pay for it ?
a) Rs 825 b) Rs 1000 c) Rs 1100 d) 1125
Ans: b) Rs 1000
9. If the S.P of Rs 24 results in a 20% discount on list price, what S.P would result in a 30% discount on list price ?
a) Rs 27 b) Rs 21 c) Rs 20 d) Rs 9
Ans: b) Rs 21
10. A shopkeeper professes to sell all things at a discount of 10%, but increases the S.P. of each article by 20%. His gain on each article is
a) 6% b) 8% c) 10% d) 12%
Ans: b) 8%