Arithmetic (UPSC) Part- I

Total Questions: 50

41. Three bells toll at intervals of 9, 12 and 15 minutes respectively. All the three begin to toll at 8 a.m. At what time will they toll together again? [2003]

(a) 8.45 a.m.
(b) 10.30 a.m.
(c) 11.00 a.m.
(d) 1.00 p.m.

Correct Answer: (c) 11.00 a.m.

Solution:Bells will toll together again at a time, which is obtained by taking L.C.M. of their individual tolling intervals.
L.C.M. of 9, 12 and 15 = 180 min
They will toll together again after 180 min, i.e., 3 hours.
Time = 8 + 3 = 11 a.m.

42. Left pan of a faulty weight weighs 100 gram more than its right pan. A shopkeeper keeps the weight measure in the left pan while buying goods but keeps it in the right pan while selling his goods. He uses only 1 kg weight measure. If he sells his goods at the listed cost price, what is his gain? [2005]

(a) 200/11 %
(b) 100/11 %
(c) 1000/9 %
(d) 200/9 %

Correct Answer: (a) 200/11 %

Solution:Let the purchased amount be 1100 kg and the cost price of 1100 kg be ₹x.
Therefore, he pays for 1000 kg and buys 1100 kg.

10/11x

Therefore, net profit = x - 10/11x = x/11

Similarly while selling, if he sells 1000 kg, he would actually be selling 900 kg at the price of 1000 kg.

Similarly, once again the profit would be ₹

x/11

Therefore, total profit = ₹

2x/11

In terms of percentage, this would be

200/11%

43. There are 6 persons; A, B, C, D, E and F. [2005]

A has 3 items more than C
D has 4 items less than B
E has 6 items less than F
C has 2 items more than E
F has 3 items more than D
Which one of the following figures cannot be equal to the total number of items possessed by all the 6 persons?

(a) 41
(b) 4
(c) 53
(d) 58

Correct Answer: (c) 53

Solution:

A = C + 3, D = B - 4, E = F - 6

2,\quad F = D + 3

On adding, we get:

$A = B - 2$

Total number of items =

If , total number of items =
For , total number of items =
For , total number of items = $= 53$

44. How many numbers are there in all from 6000 to 6999 (Both 6000 and 6999 included) having all digits same? [2006]

(a) 216
(b) 356
(c) 496
(d) 504

Correct Answer: (c) 496

Solution:

(c) Total numbers between 6000 to 6999 = 1000. Now, when all the digits are different, then thousands place is always to be filled by 6, next place by any of the remaining 9 digits and the remaining two places by any of the 8 and 7 digits respectively. So, total no. of numbers, when all digits are different = 9 ×8×7=504.
Hence, total no. of numbers, where all digits are same = total numbers - numbers where digits are different = 1000-504 = 496

45. Each of the five persons A, B, C, D and E possesses unequal number of similar items. A, B and C possesses twenty-one items in all, while C, D and E possess seven items in all. How many items do A and B possess in all? [2006]

(a) 15
(b) 17
(c) 18
(d) Data is insufficient

Correct Answer: (b) 17

Solution:

As,

For equation (II), ‘C’ can take values

1, 2 and 4 as

For $1$ ,

Similarly for $2$ ,

and for $4$ ,

46. (Each small circle represents a different station) What is the maximum number of different paths that exist between the station A and the station B? [2007]

(a) 28
(b) 31
(c) 33
(d) 35

Correct Answer: (b) 31

Solution:There are 4 routes between A to B, via P, Q, R and S.

Case I: Route via P →
A to P = 3 and P to B = 3
∴ Routes via P =

Case II: A to Q = 4 and Q to B = 3
∴ Routes via Q =

Case III: Similarly, routes via R =

Case IV: Routes via S =

∴ Total number of routes =

47. 6 equidistant vertical lines are drawn on a board. 6 equidistant horizontal lines are also drawn on the board cutting the 6 vertical lines, and the distance between any two consecutive horizontal lines is equal to that between any two consecutive vertical lines. What is the maximum number of squares thus formed? [2007]

(a) 37
(b) 55
(c) 126
(d) 225

Correct Answer: (b) 55

Solution:

There can be 5 types of squares thus formed.

Case I: Single square boxes

Single square boxes along a horizontal row = 5

Single square boxes along a vertical row = 5

Number of single square boxes =

Case II: Double square boxes

Double square boxes along horizontal × vertical =

Case III: Triple square boxes =

Case IV: Squares with 4 square boxes =

Case V: Squares with 5 square boxes =

∴ Total number of squares =

48. A person has to completely put each of three liquids: 403 litres of petrol, 465 litres of diesel and 496 litres of Mobile Oil in bottles of equal size without mixing any of the above three types of liquids such that each bottle is completely filled. What is the least possible number of bottles required? [2007]

(a) 34
(b) 44
(c) 46
(d) None of the above

Correct Answer: (b) 44

Solution:Maximum capacity of each bottle can be found by taking the H.C.F of the three given liquids.

Maximum capacity of each bottle = HCF of 403, 465, and 496 = 31

Number of bottles for 403 ℓ of petrol = 403/31 = 13

Number of bottles for 465 ℓ of diesel = 465/31 = 15

Number of bottles for 496 ℓ of mobile oil = 496/31 = 16

Hence, total number of bottles =

49. If all the numbers from 501 to 700 are written, what is the total number of times does the digit 6 appear? [2007]

(a) 138
(b) 139
(c) 140
(d) 141

Correct Answer: (c) 140

Solution:

For numbers between 600 to 700:

Number of 6 at the units place = 10

Number of 6 at the tens place = 10

Number of 6 at the hundredth place = 100

For numbers between 501 to 599:

Number of 6 at the units place = 10

Number of 6 at the tens place = 10

Hence, total number of 6s between 501 – 700:

50. The average salary of 100 employees in an office is ₹16,000 per month. The management decided to raise salary of every employee by 5% but stopped a transport allowance of ₹800 per month which was paid earlier to every employee. What will be the new average monthly salary? [2007]

(a) ₹16,000
(b) ₹16,500
(c) ₹16,800
(d) Data are insufficient

Correct Answer: (c) ₹16,800

Solution:

Since salary of each employee is increased by 5%,
Net average increase in salary = 5%

∴ New average monthly salary

As transport allowance is not a part of the salary, the deduction of ₹800 will have no effect on the new average salary.

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Arithmetic (UPSC) Part- I

41. Three bells toll at intervals of 9, 12 and 15 minutes respectively. All the three begin to toll at 8 a.m. At what time will they toll together again? [2003]

43. There are 6 persons; A, B, C, D, E and F. [2005]

44. How many numbers are there in all from 6000 to 6999 (Both 6000 and 6999 included) having all digits same? [2006]

45. Each of the five persons A, B, C, D and E possesses unequal number of similar items. A, B and C possesses twenty-one items in all, while C, D and E possess seven items in all. How many items do A and B possess in all? [2006]

46. (Each small circle represents a different station) What is the maximum number of different paths that exist between the station A and the station B? [2007]

49. If all the numbers from 501 to 700 are written, what is the total number of times does the digit 6 appear? [2007]

50. The average salary of 100 employees in an office is ₹16,000 per month. The management decided to raise salary of every employee by 5% but stopped a transport allowance of ₹800 per month which was paid earlier to every employee. What will be the new average monthly salary? [2007]

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