Arithmetic (UPSC) Part- II

Total Questions: 50

31. In a garrison, there was food for 1000 soldiers for one month. After 10 days, 1000 more soldiers joined the garrison. How long would the soldiers be able to carry on with the remaining food? [2013-II]

(a) 25 days
(b) 20 days
(c) 15 days
(d) 10 days

Correct Answer: (d) 10 days

Solution:Let the remaining food last for x days.
1000 soldiers had provisions for (30 – 10) = 20 days
(1000 + 1000) men had provisions for x days.
More men, less days (indirect proportion)
∴ 2000 : 1000 : : 20 : x
⇒ 2000 / 1000 = 20 / x × x = 10 days

32. The tank-full petrol in Arun’s motor-cycle lasts for 10 days. If he starts using 25% more everyday, how many days will the tank-full petrol last? [2013-II]

(a) 5
(b) 6
(c) 7
(d) 8

Correct Answer: (d) 8

Solution:Let ‘x’ be the initial petrol consumption. Let ‘y’ be the number of days petrol lasts for. According to question

	Petrol Consumption	Days
Initial	x	10
Final	125/100×x

Hence, it’s a case of indirect variation.

∴ x × 10 = (125 / 100) × x × y ⇒ y = 1000 / 125 = 8 days

33. There are some balls of red, green and yellow colour lying on a table. There are as many red balls as there are yellow balls. There are twice as many yellow balls as there are green ones. The number of red balls [2013-II]

(a) is equal to the sum of yellow and green balls
(b) is double the number of green balls
(c) is equal to yellow balls minus green balls
(d) cannot be ascertained.

Correct Answer: (b) is double the number of green balls

Solution:According to question
R = y and y = 2G
∴ R = 2G
Hence, the number of red balls is double the number of green balls.

34. For a charity show, the total tickets sold were 420. Half of these tickets were sold at the rate of ₹5 each, one-third at the rate of ₹3 each and the rest for ₹2 each. What was the total amount received? [2014-II]

(a) ₹900
(b) ₹1,540
(c) ₹1,610
(d) ₹2,000

Correct Answer: (c) ₹1,610

Solution:Total amount received is

= (420/2) × 5 + (420/3) × 3 + (420/6) × 2 = 210 × 5 + 140 × 3 + 70 × 2

= 1050 + 420 + 140 = ₹ 1610

35. If Sohan, while selling two goats at the same price, makes a profit of 10% on one goat and suffers a loss of 10% on the other [2014-II]

(a) he makes no profit and no loss.
(b) he makes a profit of 1%.
(c) he suffers a loss of 1%.
(d) he suffers a loss of 2%.

Correct Answer: (c) he suffers a loss of 1%.

Solution:Let C.P of 1st goat is ₹ 100.
∴ S.P. of 1st goat is ₹ 110 (10% profit)
∴ S.P. of 2nd goat is ₹ 110 (Same S.P.)

∴ C.P. of 2nd goat = (100/90) × 110 (10% loss) = 1100/9

∴ Total C.P. = 100 + (1100/9) = 2000/9

Total S.P. = 2 × 110 = 220

∴ Loss % = ((2000/9) – 220) × 100 / (2000/9)
= (20/9) × 100 / (2000/9) = 1% loss

Shortcut method: Loss %

= ((common gain and loss %)/10)² = (100/10)² = 100/100 = 1%

36. Five persons fire bullets at a target at an interval of 6, 7, 8, 9 and 12 seconds respectively. The number of times they would fire the bullets together at the target in an hour is [2014-II]

(a) 6
(b) 7
(c) 8
(d) 9

Correct Answer: (b) 7

Solution:Time gap after which they will first hit the target is given by LCM of 6, 7, 8, 9, 12.

LCM = (12 × 42) sec.
∴ In 1 hr (= 3600 sec) no. of time they will hit together is =
3600 / (12 × 42) = 50 / 7 = 7 ×1/7 times

37. A bell rings every 18 minutes. A second bell rings every 24 minutes. A third bell rings every 32 minutes. If all the three bells ring at the same time at 8 o’clock in the morning, at what other time will they all ring together? [2014-II]

(a) 5
(b) 6
(c) 7
(d) 8

Correct Answer: (d) 8

Solution:LCM of 18, 24, 32
LCM of 9, 12, 16
LCM = 3 × 4 × 3 × 4 = 144 min
= 144 / 60 = 2 × 4/5 hr = 2 hrs 24 min

∴ Bell will ring together again after 2 × (2 hrs 24 min)
= 4 hrs. 48 min
i.e., 12 : 48 hrs

38. As per agreement with a bank, a businessman had to refund a loan in some equal instalments without interest. After paying 18 instalments he found that 60 percent of his loan was refunded. How many instalments were there in the agreement? [2014-II]

(a) 22
(b) 24
(c) 30
(d) 33

Correct Answer: (c) 30

Solution:Let amount in each installment = x
Let total amount paid = L According to Question.
∴ 18x = (60 / 100) × L
⇒ L / x = (100 × 18) / 60 = 30 = no. of instalments.

39. In a town, 45% population read magazine A, 55% read magazine B, 40% read magazine C, 30% read magazines A and B, 15% read magazines B and C, 25% read magazines A and C; and 10% read all the three magazines. What percentage do not read any magazine? [2015-II]

(a) 10%
(b) 15%
(c) 20%
(d) 25%

Correct Answer: (c) 20%

Solution:

Number of population who read the magazine
= (45 + 55 + 40) – (30 + 25 + 15) + 10
= 140 – 70 + 10 = 80%
Number of population who do not read magazine
= 100 – 80 = 20%

40. Two equal glasses of same type are respectively 1/3 and 1/4 full of milk. They are then filled up with water and the contents are mixed in a pot. What is the ratio of milk and water in the pot? [2015-II]

(a) 7 : 17
(b) 1 : 3
(c) 9 : 21
(d) 11 : 23

Correct Answer: (a) 7 : 17

Solution:Let the capacity of each of the equal glass = x litre
Each glass containing x/3l and x/4l of milk.
The quantities of milk in first and the second glasses were

x/3 and x/4 respectively

= (x/3 + x/4) = (4x + 3x)/12 = 7x/12 l

So, the quantities of water in the first and the second glasses
were

= (x – x/3) l and (x – x/4) l = 2x/3 + 3x/4 = (8x + 9x)/12 = 17x/12 l

Ratio of milk and water = 7x/12 : 17x/12 = 7 : 17

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