UP Lekhpal 2015 Answer Key and Solved Question Paper

Answer: A. 8.68 cm

Explanation:

2Ï€r = 18.6 + (D)
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

Answer: C. 348

Explanation:

Given data: LCM = 2448 , HCF = 12 and
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              — eqn. (1)

a – b = 60 ; given in question

as, (a – b)² = a² + b² – 2ab and

as (a + b)² = a² + b² + 2ab
(a + b)² = (a – b)² + 4ab
(a + b)² = 60X60 + 4X29376
(a + b)² = 121104
(a + b) = √(121104)
(a + b) = 348

Sum of two numbers = 348

Answer: D. Rs. 5250

Explanation:

If price of moped = x, then the price of scooter = x+4200.

Now,

(x+4200) : x = 9 : 5

9x = 5(x +4200)
9x = 5x + 21,000
4x = 21,000
x = 21,000/5 => 5250.

Answer: B. 192

Explanation:

Let the three numbers are A, B, C. Then,

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

Answer: D. 9720 sq.metre

Answer: C. 10 m

Explanation:

The perimeter of a top surface of e rectangular table = 28 m

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

Then, 2(l + b) = 28
l + b = 28/2
l + b = 14        ……………………………………………….. (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 + b²) /b = 14
48 + b² = 14b
b² – 14b + 48 = 0
b² – 8b – 6b + 48 = 0
b (b – 8) – 6 (b – 8) = 0
(b – 8) (b – 6) = 0
b – 8  = 0  &  b – 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 = (8² + 6²)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.

Answer: A. 5 cm

Explanation:

The perimeter of a triangle = 30 cm
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 – 13
a + b = 17          ………….. (1)
Put the value of a = 60/b in equation (1),
60/b + b = 17
60 + b2 = 17 b
b2 – 17 b + 60 = 0
b2 – 12b – 5 b+ 60
b (b – 12) – 5 (b – 12) = 0
(b – 12) (b – 5) = 0
b – 12 = 0 & b – 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.

Answer: B. 600

Explanation:

The radius of a wheel = 21 cm
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

Answer: A. 28 days

Answer: A. 60 litres

Explanation:

The ratio of the acid and water in a mixture = 2: 1
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