Question 1

( 0. 6 + . 7 + . 8 + . 3) =?

Accepted Answer

0.6 + . 7 + .8 + .3 = ( 6/9 + 7/9 + 8/9 + 3/9) = 24 / 9 = 8 / 3 = 22/3

Question 2

If 1.5 x a = 0.04 x b then the value of (b - a) / ( b + a) is?

Accepted Answer

a / b = 0.04 / 1.5 = 4 / 150 = 2 / 75 ∴ Given Exp. (b - a) / ( b + a) = (1- a/b ) / (1 + a/b) = (1- 2 / 75) / (1 + 2 / 75) = ( 73/75 ) / ( 77/75) = 73/77

Question 3

If √ 0.05 x 0.5 x a = 0.5 x 0.05 x √b, then a/b =?

Accepted Answer

Given expression = √0.5 x .5 x a = .5 x .05 x √ b ⇒ √.025 x a = 0.25 x ⇒ b ⇒ 0.025a = 0.25 x .025 x b ∴ a/b = (.025 x .025) /.025 = .025

Question 4

(.23 - .023) / ( .0023 / 23 ) =?

Accepted Answer

Given expression = (.23 - .023) / ( .0023 / 23 ) = .207 / (.0023 / 23) = .207 / .0001 =.2070 / .0001 = 2070

Question 5

[(3.537 - .948) 2 + (3.537 + .948) 2] / [(3.537) 2 + (.948) 2] =?

Accepted Answer

Given expression = [(3.537 - .948)2 + (3.537 + .948)2] / [(3.537)2 + (.948)2] = [(a - b)2 + (a + b)2] / (a2 + b2) (Where a = 3.537 and b = 0.948) = 2(a2 +b2) / (a2 +b2) = 2

Question 6

(6.5 x 4.7 + 6.5 x 5.3 ) / (1.3 x 7.9 - 1.3 x 6.9) =?

Accepted Answer

Given Expression = (6.5 x 4.7 + 6.5 x 5.3 ) / (1.3 x 7.9 - 1.3 x 6.9) = [6.5 x (4.7 + 5.3 )] / [13 x (7.9 - 6.9)] = (6.5 x 10) / (1.3 x 1) = 50

Question 7

The greatest fraction out of 2/5, 5/6, 11/12 and 7/8 is?

Accepted Answer

2/5 = 0.4 , 5/6 = 0.833, 11/12 = 0.916 and 7/8 = 0.875 Clearly, the greatest fraction is 0.916, i, e . 11/12.

Question 8

[ .6 x .6 x .6 x .4 x .4 x .4 + 3 x .6 x .4 x (.6 + .4 )] =?

Accepted Answer

Given expression =(.6)3 + (.4) 3 + 3 x .6 x .4 x (.6 + .4) = a3 + b3 + 3ab (a+b) = (a+b)3 = (.6 + .4)3 = 13 = 1

Question 9

(.58 x .58 x .58 - .42 x .42 x .42 - 3 x .58 x .42 x .16) =?

Accepted Answer

Given Expression = (.53)3 - (.42)3- 3 x .58 x .42 x (.58-.42) = a3-b3 -3ab(a - b) = (a - b)3 (where a = .58 and b=.42) = (.58 - .42 )3 = .16 x .16 x .16 = 0.004096

Question 10

If 3 is added to the denominator of a fraction, it becomes 1/3 and if 4 be added to its numerator, It becomes 3/4, then fraction is?

Accepted Answer

Let the required fraction be p/q ∵ p / (q + 3) = 1/3 ⇒ 3p - q = 3 ...(i) and, (p + 4) / q = 3/4 ⇒ 4p - 3q = -16 ...(ii) Solving these equations, we get p = 5, q = 12 ∴ Required fraction = 5/12

Question 11

If the numerator of a fraction is increased by 2 and the denominator is increased by 1, the fraction because 5/8 and if the numerator of the same fraction is increased by 3 and the denominator is increased by 1, the fraction becomes 3/4 . What is th…

Accepted Answer

Let the original fraction be p/q Then, (p + 2) / (q + 1) = 5/8 ⇒ 8p - 5q = 11 .....(i) Again (p + 3) / (q + 1) = 3/4 ⇒ 4p - 3q = 9 ...(ii) Solving equations , (i) and (ii), we get , p = 3 and q = 7 ∴ Fraction = 3/7

Question 12

If the numerator of a fraction is increased by 2 and denominator is increased by 3, the faction becomes 7/9 and if numerator as well as denominator are decreased by 1, the fraction becomes 4/5. What is the original fraction?

Accepted Answer

Let the numerator and denominator be p and q respectively. Then, (p + 2) / (q + 3) = 7/9 ⇒ 9(p + 2) = 7(q +3) ⇒ 9p - 7q = 3 ....(i) Again, (p - 1) / (q - 1) = 4/5 ⇒ 5p - 4q = 1 ....(ii) Solving (i) and (ii) we get, p = 5, q = 6 Required fraction = 5/6

Question 13

If a fraction's numerator is increased by 1 and the denominator is increased by 1 and denominator is increased by 2 then the fraction becomes 2/3. But when the numerator is increased by 5 and the denominator is increased by 1, then the fraction beco…

Accepted Answer

Let the numerator and denominator be p and q respectively. Then, (p + 2) / (q + 3) = 7/9 ⇒ 9(p + 2) = 7(q +3) ⇒ 9p - 7q = 3 ....(i) Again, (p - 1) / (q - 1) = 4/5 ⇒ 5p - 4q = 1 ....(ii) Solving (i) and (ii) we get, p = 5, q = 6 Required fraction = 5/6

Question 14

The value of (9 2 x 18 4) / 3 16 is?

Accepted Answer

Given expression = [(32)2 x (3 x 3 x 2)4] / 316 = (34 x 38 x 24) / 316 = 24 / 34 = 16 / 81

Question 15

A man spends (1/7)th of his salary on food, half of the remaining on clothing and (1/3)rd of the remaining on entertainment. He is still left with Rs. 600. How much does he spend on entertainment?

Accepted Answer

Let man's salary be Rs. N Money spend on food =N/7 Money spends on clothing = (N - N/7) x 1/2 = (6N/7) x (1/2) =3N/7 Money spend on entertainment = (N - N/7 - 3N/7)/3 = (7N - 4N)/7 = N/7 Now, money left =600 ⇒ N - N/7 - 3N/7 - N/7 = 600 ⇒ 7N - 5N/7 = 600 ⇒ N = 600 x 7/2 = Rs. 2100 ∴ Money spend on entertainment = 1/7 x 2100 = Rs. 300

Question 16

If a fraction is multiplied by itself and then divided by the reciprocal of the same fraction, the result is 18 26/ 27. find the fraction?

Accepted Answer

If the required fraction be N. Then, (N x N) / (1/N) = 1826/27 ⇒ N3 = 512 / 27 ∴ N = 8/3 = 22/3

Question 17

A lamppost is divided into three parts, the first part is (1/3)rd of the whole length, second (3/8)th of the first and the third is 6 m 50 cm. The length of the lamppost is?

Accepted Answer

Let the length of lamppost = L m Then,first part = L/3 and second part = (3/8) x L/3 = L/8 and third part = 6 m 50 cm = 6.50 m First part + second part + Third part = length of lamppost ⇒ L/3 + L/8 + 6.5 = L ⇒ L - L/3 - L/8 =6.5 ⇒ (24L - 8L - 3L)/24 = 6.5 ⇒ 13L/24 = 6.5 ∴ L = (65.x 24)/13 = 12 m

Question 18

Find the value of 27 x 1. 2 x 5.526 2 x 0. 6 .

Accepted Answer

27 x 1.2 x 5.5262 x 0.6 = 27 x [(12 - 1) / 9] x [(55262 - 5526)/9000] x (6/9) = (27 x 11)/9 x (49736/9000) x (6/9) = 1094192 / 9000 = 121.576888... = 121.5768

Question 19

How many pieces of 13.2 cm can be cut from a 330 cm long rod?

Accepted Answer

Total length of the rod = 330 cm Length of a piece = 13.2 cm. Required number of pieces = Total length/Length of a piece ; Required number of pieces = 330/13.2 = 25

Question 20

1/8th part of a pencil is black, half of the remaining is white. If the remaining part is blue and length of this blue part is 3 1/ 2cm, then find the length of the pencil?

Accepted Answer

Let the total length of pencil = L cm Then, black part = L/8 ∴ Remaining part = L - L/8 = 7L/ 8 and White part = (7L/8)/2 = 7L/8 ∴ Remaining part = L - (L/8 + 7L/16) = 7L/16 ∴ length of blue part = 7L/16 According to the question, 7L/16 = 31/2 ⇒ 7L/16 = 7/2 ∴ L =8

Decimal Fraction Questions