Question 1

(69842 x 69842 - 30158 x 30158) / (69842 - 30158) =?

Accepted Answer

Given expression = [(69842)2 - (30158)2] / [(69842 - 30158)] = [ (69842 - 30158) (69842 + 30158) ] / (60842 - 30158) = 100000

Question 2

31/10 x 3/10 + 7/5 ÷ 20 =?

Accepted Answer

Given expression = 93/100 + 7/5 x 1/20 = 93/100 + 7/100 = 1

Question 3

The value of 1 + 1/(4 x 3) + 1/(4 x 3 2) +1/(4 x 3 3) up to four places of decimals is?

Accepted Answer

Given expression = (108 + 9 + 3 +1) / 108 = 121 / 108 = 1.1203

Question 4

(1/5 ÷ 1/5 of 1/5) / (1/5 of 1/5 ÷ 1/5) =?

Accepted Answer

Given expression = (1/5 ÷ 1/25 ) / (1/25 ÷ 1/5) = (1/5 x 25) / (1/25 x 5) = 5 x 5 = 25

Question 5

(1/4 + 1/4 ÷ 5/4) / (1/4 x 1/4 + 2 1/ 4) =?

Accepted Answer

Given expression = (1/4 + 1/4 x 4/5) / (1/16 + 9/4) = (1/4 + 1/5) / (37/16) = 9/20 x 16/37 = 36/185

Question 6

In a college 1/5th of the girls and 1/8th of the boys took part in a social camp. What of the total number of student in the college took part in the camp?

Accepted Answer

Out of the 5 girls, 1 took part in the camp. Out of the 8 boys, 1 took part in the camp. ∴ 2/13 of total number of students took part in the camp.

Question 7

(4.59 x 1.8 ÷ 3.6 + 5.4 of 1/9 - 1/5) =?

Accepted Answer

Given Exp. = 4.59 x 1.8 / 3.6 + 0.6 - 0.2 = 2.295 + 0.6 - 0.2 = 2.695

Question 8

(1/2 ÷ 4 + 20) / (1/2 x 4 + 20) =?

Accepted Answer

Given Exp. = (1/2 x 1/4 + 20) / (2 + 20) = (161/8) x (1/22) = 161 / 176

Question 9

[1/(1.2.3)] + [1/(2.3.4)] + [1/(3.4.5)] + [1/(4.5.6)] is equal to

Accepted Answer

Given Exp. = [(4 x 5 x 6) + (5 x 6) + (2 x 6) + (2 x 3)] / [(2 x 3 x 4 x 5 x 6)] = 168 / (24 x 30) = 7 / 30

Question 10

3 2/ 3 + 2 3/ 4 + 1 1/ 2 =?

Accepted Answer

? = 32/3 + 23/4 + 11/2 = 3 + 2 + 1 + (2/3 + 3/4 + 1/2) = 6 + (8 + 9 + 6)/12 = 6 + (23/12) = 6 + (111/12) = 711/12

Question 11

(5568 / 87) 1/3 + (72 x 2) 1/2 = (?) 1/2?

Accepted Answer

(?)1/2 = (5568 / 87)1/3 + (72 x 2)1/2 = (64)1/3 + (144)1/2 ∴ ? = (4 + 12)2 = 256

Question 12

√ 289 - √ 625 ÷ √ 25 is equal to?

Accepted Answer

√289 - √625 ÷ √25 = √17 x 17 - √25 x 25 ÷ √5 x 5 = 17 - 25 ÷ 5 = 17 - 5 = 12

Question 13

If 0.764 B = 1.236 A, then what is the value of (B - A)/(B + A)?

Accepted Answer

Given, 0.764 B = 1.236 A ⇒ B/A = 1.236 / 0.764 Now, (B - A)/(B + A) = (B/A - 1) / (B/A + 1) = (1.236/0.764 - 1) / (1.236/0.764 + 1) = (1.236 - 0.764)/(1.236 + 0.764) = 0.472/2.000 = 0.236

Question 14

7059 - 2350 + 1936 =? x 50

Accepted Answer

7059 - 2350 + 1936 = ? x 50 ⇒ 8995 - 2350 = ? x 50 ⇒ ? = 6645/50 = 132.9

Question 15

What is 786 time of 964?

Accepted Answer

Required number = 786 x 964 = 757704

Question 16

5/8 x 2 3/ 5 ÷ 4/9 =?

Accepted Answer

? = 5/8 x 23/5 ÷ 4/9 = 5/8 x 13/5 x 9/4 = 117/32 = 321/32

Question 17

(4 x 4 x 4 x 4 x 4 x 4) 5 x (4 x 4 x 4) 8 ÷ (4) 3 = (64) ?

Accepted Answer

(4 x 4 x 4 x 4 x 4 x 4)5 x (4 x 4 x 4)8 ÷ (4)3 = (64)? ⇒ (46)5 x (43)8 x 1/(4)3 = (43)? ⇒ (4)30 x (4)24/(4)3 = (4)3 x ? ⇒ 430 + 24 - 3 = 43 x ? ⇒ 451 = 43 x ? ⇒ 3 x ? = 51 ∴ ? = 51/3 = 17

Question 18

√ 132 + 28 ÷ 4 - (3)3 + 107 = (?) 2

Accepted Answer

(?)2 √132 + 28 ÷ 4 - (3)3 + 107 = √169 + 7 - 27 + 107 = √256 = 16 ∴ ? = √16 = 4

Question 19

√ 289 - √ 625 ÷ √ 25 is equal to?

Accepted Answer

√289 - √625 ÷ √25 = √17 x 17 - √25 x 25 ÷ √5 x 5 = 17 - 25 ÷ 5 = 17 - 5 = 12

Question 20

If 0.764 x P = 1.236 x Q, then what is the value of (Q - P) / (Q + P)?

Accepted Answer

Given, 0.764 x P = 1.236 x Q ⇒ Q / P = 1.236 / 0.764 Now, (Q - P) / (Q + P) = [(Q/P) - 1] / [(Q/P) + 1] ⇒ [(1.236/0.764) - 1] / [(1.236/0.764) + 1] = (1.236 - 0.764) / (1.236 + 0.764) = 0.472 / 2.000 = 0.236

Simplification Questions