# UP Lekhpal 2015 Answer Key and Solved Question Paper

## Previous Examinations : UP Lekhpal 2015 Set B

UP Lekhpal question paper and answer keys of 2015 exam held on 13th Sep 2015 are available here. You can download pdf of fully solved question paper of UP Lekhpal 2015 from here.**1.**If the circumference of a circle is 18.6 cm more than its diameter, then what is the diameter of the circle ?

**Answer: ** A. 8.68 cm

**Explanation: **

2Ï€r = 18.6 + 2r

2Ï€r - 2r = 18.6

2r (Ï€ - 1) = 18.6

2r = 186/10 X 7/15

r = 186/10 X 7/15 X 1/2

=> 1302/300

D = 2 X 1302/300 = 8.68

**2.**The HCF and LCM of two numbers are 12 and 2448 respectively. If the difference of the numbers is 60, then the sum of the numbers is ?

**Answer: ** C. 348

**Explanation: **

difference of numbers = 60

We know that,

LCM x HCF of two numbers = Multiplication of both numbers

Let a and b are two numbers, Then

a X b = LCF X HCF

a X b = 12 X 2448 = 29376 â€” eqn. (1)

a â€“ b = 60 ; given in question

as, (a â€“ b)

^{2}= a

^{2}+ b

^{2}â€“ 2ab and

as (a + b)

^{2}= a

^{2}+ b

^{2}+ 2ab

(a + b)

^{2}= (a â€“ b)

^{2}+ 4ab

(a + b)

^{2}= 60X60 + 4X29376

(a + b)

^{2}= 121104

(a + b) = âˆš(121104)

(a + b) = 348

Sum of two numbers = 348

**3.**The prices of a scooter and a moped are in the ratio9:5. If a scooter costs Rs. 4200 more than a moped, then the price of the moped is ?

**Answer: ** D. Rs. 5250

**Explanation: **

Now,

(x+4200) : x = 9 : 5

9x = 5(x +4200)

9x = 5x + 21,000

4x = 21,000

x = 21,000/5 => 5250.

**4.**The sum of three numbers is 392. If the ratio of first number to second number is 2:3 and the ratio of second number to third number is 5:8, then the third number is ?

**Answer: ** B. 192

**Explanation: **

A:B = 2:3 and B:C = 5:8 = ( 5 x 3/5) : ( 8 x 3/5) = 3 : 24/5

Hence, A:B:C = 2:3:24/5 => 10:15:24

C = 392 x 24/49 => 192

**5.**The perimeter of a triangular field is 540 meters and the ratio of its sides is 5:12:13. What will be the area of this field ?

**Answer: ** D. 9720 sq.metre

**6.**The perimeter of a top surface of a rectangular table is 28 m and its area is 48 m^2. What is the length of the hypotenuse of the table ?

**Answer: ** C. 10 m

**Explanation: **

Formula-

The perimeter of the rectangular table = 2 (l + b)

Then, 2(l + b) = 28

l + b = 28/2

l + b = 14 â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦.. (1)

Area of surface of the rectangular table = 48 m2

Then, lb = 48

l = 48/b

Put the value of l = 48/b in equation (1),

Then, 48/b + b = 14

(48 + b

^{2}) /b = 14

48 + b

^{2}= 14b

b

^{2}â€“ 14b + 48 = 0

b

^{2}â€“ 8b â€“ 6b + 48 = 0

b (b â€“ 8) â€“ 6 (b â€“ 8) = 0

(b â€“ 8) (b â€“ 6) = 0

b â€“ 8 = 0 & b â€“ 6 = 0

b = 8 & b = 6

Then, l = 48/6 = 8

l = 8 cm & b = 6 m

Hypotenuse of the rectangular surface of the table = (8

^{2}+ 6

^{2})1/2

= (64 + 36)1/2

= (100)1/2

= 10 m

Then, the hypotenuse of the table is 10 m.

Hence, the answer is (3) 10 m.

**7.**The perimeter of a triangle is 30 cm and its area is 30 cm

^{2}. If the length of the largest side of the triangle is 13 cm, then what is the smallest side of the triangle ?

**Answer: ** A. 5 cm

**Explanation: **

the area of a triangle = 30 cm2

Then, ab/2 = 30

ab = 30 x 2

ab = 60 cm

a = 60/b

The a + b + 13 = 30

a + b = 30 â€“ 13

a + b = 17 â€¦â€¦â€¦â€¦.. (1)

Put the value of a = 60/b in equation (1),

60/b + b = 17

60 + b2 = 17 b

b2 â€“ 17 b + 60 = 0

b2 â€“ 12b â€“ 5 b+ 60

b (b â€“ 12) â€“ 5 (b â€“ 12) = 0

(b â€“ 12) (b â€“ 5) = 0

b â€“ 12 = 0 & b â€“ 5 = 0

b = 12 and b = 5

Then, the sides of the triangle are 5, 7 and 13.

Then, the smallest side of the triangle is 5.

**8.**The radius of the wheel is 21 cm. How many rounds will it take to cover the distance of 792 metres ?

**Answer: ** B. 600

**Explanation: **

Then, the circumference of the wheel = (2 x 22 x 21)/7

= 2 x 22 x 3

= 132 cm

The distance covered by wheel in a round = 132 cm

Total distance covered by the wheel = 792 m

1 m = 100 cm

Therefore, 792 m = 792 x 100 = 79200 cm

Then, the number of rounds of the wheel to cover the distance 79200 cm = 79200/132

= 600

**9.**A man is twice as fast as a woman and a woman is twice as fast as a boy. If all of them i.e, a man, a woman and a boy can finish a work together is 4 days, in how many days will a boy do it alone ?

**Answer: ** A. 28 days

**10.**In a mixture of 60 litres, the ratio of acid and water is 2:1. What amount of water must be added to make the ration of acid and water as 1:2 ?

**Answer: ** A. 60 litres

**Explanation: **

Total quantity of mixture = 60 litres

Then, the of acid in the mixture = 60 x 2/3

= 40 litres

The, quantity of water in the mixture = 60 x 1/3

= 20 litres

If water 60 litres added, then the ratio will be 1:2

Then, the new ratio of acid and water = 40 : (20+40)

= 40 : 80

= 1:2

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