Question 1

A 120 m long rope is cut into 3 equal parts. What is the length of each part?

Accepted Answer

Required length = 120/3 = 40 m

Question 2

A number when multiplied by five times of itself give the value equal to 1445. What is the number?

Accepted Answer

Let the number = a According to the question, a x 5a = 1445 5a2 = 1445 ∴ a2= 1445/5 =289 ∴ a= √289 = 17

Question 3

A board 80 inches long is divided into 4 equal parts. What is the length of each part?

Accepted Answer

Required length = 80/4 = 20 inches

Question 4

If a * b = a + b + a/b, Then the value of 12 * 4 is

Accepted Answer

Since a * b = a + b + a/b ∴ 12 * 4 = 12 + 4 + 12/4 = 12 + 4 + 3 = 19

Question 5

[137 x 137 + 137 x 133 + 133 x 133] / [137 x 137 x 137 - 133 x 133 x 133] =?

Accepted Answer

Given exp. = [ a2 + ab + b2 ] / [a3 - b3] where a = 137, b = 133 = 1/(a - b) = 1/(137- 133) =1/4

Question 6

(117 x 117 x 117 - 98 x 98 x 98) / (117 x 117 + 117 x 98 + 98 x 98) =?

Accepted Answer

Given expression = (a3 - b3) / (a2 + ab + b2), where a=117, b =98 = [(a-b)(a2 + ab + b2)] / (a2+ab+b2) =(a-b) =117 - 98 = 19.

Question 7

(343 x 343 x 343 + 257 x 257 x 257 ) / (343 x 343 - 343 x 257 + 257 + 257) =?

Accepted Answer

Given Exp. = ( a3 + b3 ) / ( a2 - ab + b2 ), where a =3 42, b = 257 = [(a + b )(a2 - ab +b2)] / (a2 - ab + b2) = a + b = 343+257 = 600.

Question 8

3 ÷ [(8 - 5) ÷ {(4 - 2) ÷ (2 + 8/13)}] =?

Accepted Answer

Given expression = 3 ÷ [(8 - 5) ÷ {(4 - 2) ÷ (2 + 8/13)}] = 3 ÷ [3 ÷ { 2 ÷ 34/13}] = 3 ÷ [3 ÷ { 2 x 13/34}] = 3 ÷ [ 3 x 17/13] = 3 x 13/51 = 13/17

Question 9

{7 1/ 2 + 1/2 ÷ 1/2 of 1/4 - 2/5 x 2 1/ 3 ÷ 1 7/ 8 of (1 2/ 5 - 1 1/ 3) } =?

Accepted Answer

Given expression = 15/2 + 1/2 ÷ 1/8 - 2/5 x 7/3 ÷ 15/8 x (7/5 - 4/3) = 15/2 + 4 - 2/5 x 7/3 ÷ 15/8 x 1/15 = 15/2 + 4 - 2/5 x 7/3 ÷ 1/8 = 15/2 + 4 - 2/5 x 7/3 x 8/1 = 15/2 + 4 - 112/15 = 23/2 - 112/15 = 121/30 = 41/30

Question 10

3/4 ÷ 2 1/ 4 of 2/3 - [(1/2 - 1/3) / (1/2 + 1/3) x 3 1/ 3 + 5/6 =?

Accepted Answer

Given expression = 3/4 ÷ 9/4 of 2/3 - [(1/6) / (5/6)] x 10/3 + 5/6 = 3/4 x 2/3 - 1/6 x 6/5 x 10/3 + 5/6 = 1/2 - 2/3 + 5/6 = (3 - 4 + 5) / 6 = 4 / 6 = 2 /3

Question 11

5/6 ÷ 6/7 x? - 8/9 ÷ 1 3/ 5 + 3/4 x 3 1/ 3 = 2 7/ 9

Accepted Answer

Let 5/6 ÷ 6/7 x N - 8/9 ÷ 8/5 + 3/4 x 10/3 = 25 / 9 Then, 5/6 x 7/6 x N - 8/9 x 5/8 + 5/2 = 25/9 ⇒ 35N / 36 = 25/9 + 5/9 - 5/2 ⇒ 35N / 36 = (50 + 10 - 45) / 18 = 5/6 ∴ N = (5/6 x 36/35) = 6/7

Question 12

15 2/ 3 x 3 1/ 6 + 6 1/ 3 = 11 7/ 18 +?

Accepted Answer

Let 47/3 x 19/6 + 19/3 = 205 / 18 + N Then, N = 893/18 + 19/3 - 205/18 ⇒ N = 893 + 114 - 205 / 18 ∴ N = 802 / 18 = 445/9

Question 13

7 1/ 2 - [ 2 1/ 4 ÷ { 1 1/ 4 - 1/2(1 1/ 2 - 1/3 - 1/6)}] is equal to?

Accepted Answer

Given expression = 15/2 -[9/4 ÷ {5/4 - 1/2(3/2 - 1/3 - 1/6)}] = 15/2 -[9/4 ÷ {5/4 - 1/2 x 1}] = 15/2 -[9/4 ÷ {5/4 - 1/2}] = 15/2 -[9/4 ÷ 3/4] = 15/2 - [9/4 x 4/3] = (15/2 - 3) = 9 / 2 = 41/2

Question 14

50 /? =? / 12 1/ 2

Accepted Answer

Let 50 / N = N / (25/2) ⇒ N2 = 50 x 25/2 = 625 ∴ N = √625 = 25

Question 15

If x/y = 4/5, then the value of 4/7 + (2y - x)/(2y + x) is?

Accepted Answer

Given Exp. = 4/7 + (2y - x)/(2y + x) = 4/7 + [(2 - (x/y)] / [2 + (x/y)] = 4/7 + [2 - 4/5] / [2 + 4/5] = 4/7 + ( 6/5 x 5/14 ) = 4/7 + 3/7 = 1

Question 16

If x/2y = 3/2, the value of (2x + y) / (x - 2y) equals?

Accepted Answer

Given expression = 2x + y / x - 2y Dividing Num and Denom by y we get. = [2(x/y) + 1] / [(x/y) - 2] = (2 x 3 + 1) / (3 - 2) = 7/1 = 7 [ ∵ x/2y = 3 / 2 ⇒x/y = (3 / 2 x 2) = 3 ]

Question 17

(885 x 885 x 885 + 115 x 115 x 115) / (885 x 885 + 115 x 115 - 885 x 115) is equal to?

Accepted Answer

Given expression = (a3 + b3) / (a2 + b2 - ab) = (a + b)(a2 + b2 - ab) / (a2 + b2 - ab) = (a + b) = (885 + 115) = 1000

Question 18

4 2/ 17 ÷ 1 2/ 5 x 2 2/ 33 =?

Accepted Answer

Give expression = 70/17 ÷ 7/5 x 68/33 = 70/17 x 5/7 x 68/33 = 200/33 = 62/33

Question 19

If a/b = 1/3, then (3a + 2b) / (3a - 2b) is equal to?

Accepted Answer

Given expression = (3a + 2b) / (3a - 2b) = [3(a/b) + 2] / [3(a/b) - 2] = [3 x 1/3 + 2] / [3 x 1/3 - 2] = 3 / -1 =-3

Question 20

When Simplified, the product (2 - 1/3) (2 - 3/5) (2 - 5/7) ... (2 - 999/1001) is equal to?

Accepted Answer

Given expression = 5/3 x 7/5 x 9/7 x ... x 1003/1001 = 1003/3

Simplification Questions