Arithmetic (UPSC) Part- V

Total Questions: 50

1. The difference between a 2-digit number and the number obtained by interchanging the positions of the digits is 54. [2021-II]

Consider the following statements:

  1. The sum of the two digits of the number can be determined only if the product of the two digits is known.
  2. The difference between the two digits of the number can be determined.
    Which of the above statements is/are correct?
Correct Answer: (b) 2 only
Solution:Let number is 10x + y
then, 10x + y - (10y + x) = 54
x - y = 6

2. X said Y, "At the time of your birth I was twice as old as you are at present." If the present age of X is 42 years, then consider the following statements: [2021-II]

  1. 8 years ago, the age of X was five times the age of Y.
  2. After 14 years, the age of X would be two times the age of Y.

Which of the above statements is/are correct?

Correct Answer: (b) 2 only
Solution:Present age of x = 42 year
and y age is y years
then 42 - y = 2y
y = 14 years
1. 8 years ago, x - age = 42 - 8 = 34
8 years ago y - age = 14 - 8 = 6
34 = 6 × 5 + 74
So, statement 1 is not correct
2. After 14 years
x's age = 42 + 14 = 56 years
y's age = 14 + 14 = 28
Now, 28 × 2 = 56
Hence, 2 is correct

3. If the price of an article is decreased by 20% and then the new price is increased by 25%, then what is the net change in the price? [2021-II]

Correct Answer: (a) 0%
Solution:Net change in price
when decrease by x% and increase
by y% = y - x - xy/100 = 25 - 20 - 20×25/100 = 0%

4. When a certain number is multiplied by 7, the product entirely comprises ones only (1111...). [2021-II]

What is the smallest such number?

Correct Answer: (d) 15873
Solution:Product of 15873 × 7 = 111111
Hence, least number = 15 873

5. A man completes 7/8 of a job in 21 days. How many more days will it take him to finish the job if quantum of work is further increased by 50%? [2021-II]

Correct Answer: (d) 15
Solution:Time required to complete the
work = 21×8/7 = 24 days
when work is incresed by 50%

then, amount of work = 1 + 1 × 50/100 = 1.5 work

Time required to finish
= 24 × 1.5 = 36 days
Extra = 36 – 21 = 15 day

6. There are three Points P, Q and R on a straight line such that PQ: QR = 3:5. If n is the number of possible values of PQ: PR, then what is n equal to? [2021-II]

Correct Answer: (b) 2
Solution:

Possible value of n = 2

7. Consider the following statements: [2021-II]

  1. The sum of 5 consecutive integers can be 100.
  2. The product of three consecutive natural numbers can be equal to their sum.

Which of the above statements is/are correct?

Correct Answer: (c) Both 1 and 2
Solution:1. Let five consecutive integers are (n – 2), (n – 1), n,
(n + 1) and (n + 2).
then, 5n = 100 ⇒ n = 20.
2. Product of three consecutive natural numbers = Sum of
the same number ⇒ 1 × 2 × 3 = 1 + 2 + 3 = 6.
Hence, both (1) and (2) are true.

8. An amount of money was distributed among A, B and C in the ratio p : q : r. [2021-II]

Consider the following statements:

  1. A gets the maximum share if p is greater than (q + r).
  2. C gets the minimum share if r is less than (p + q).

Which of the above statements is/are correct?

Correct Answer: (a) 1 only
Solution:If P > (q + r).
then, P/(P + q + r) > (q + r)/(P + q + r)
Hence, A gets maximum share.

9. Jay and Vijay spent an equal amount of money to buy some pens and special pencils of the same quality from the same store. If Jay bought 3 pens and 5 pencils, and Vijay bought 2 pens and 7 pencils, then which one of the following is correct? [2021-II]

Correct Answer: (c) The price of a pen is two times the price of a pencil
Solution:Let cost pen and pencil are x and y respectively.
then, 3x + 5y = 2x + 7y; x = 2y.
Hence, cost of pen = 2x cost of pencil.

10. P scored 40 marks more than Q in an examination. If Q scored 10% less marks than P, then how much did Q score? [2021-II]

Correct Answer: (a) 360
Solution:Let Q score = x.
then, P score = (x + 40)
According to the question.
((x + 40) – x)/(x + 40) × 100 = 10.; (40)/(x + 40) × 100 = 10
x + 40 = 400; x = 360.