Solved Questions on Fractions
1. A rope of length 5 ? metres is divided into five equal parts. What is the length of each part so obtained?
a) 12 metres
b) 32 metres
c) 52 metres
d) 72 metres
Answer: d) 1.72 metres
Explanation: Total length of rod = 5 ? metres
A rod is divided into five equal parts.
Length of each part = 5 ? metres ÷ 5
= 43/5 ÷ 5
= 43/5 × 1/5
= 43/25
= 11825 metres
= (1 + 1825) metres
= (1 + 18 × 425 × 4) metres [Mutiplied by 4 to get denominator 100, to find decimals.]
= (1 + 72100) metres
= (1 + 0.72) metres
= 1.72 metres
2. A car runs 54 ¼ km consuming 2 litres of petrol. How much distance will it take to consume 127 litre of petrol?
a) 34 ? km
b) 34 ? km
c) 34 ? km
d) 34 ? km
Answer: d) 34 ? km
Explanation: Distance covered by consuming 2 litres of petrol = 54 ¼ km = 217/4 km
Distance covered by consuming 1 litre of petrol = 217/4 km ÷ 2
= 217/8 km
Distance covered by consuming 127 litre of petrol = 217/8 km × 127 litre
= 217/8 km × 9/7
= 279/8 km
= 34 ? km
3. By how much does the sum of 37.786 and 29.576 exceed the sum of 38.789 and 23.548?
a) 015
b) 025
c) 105
d) 125
Answer: b) 5.025
Explanation: Sum of 37.786 and 29.576 = 67.362
Sum of 38.789 and 23.548 = 62.337
Difference (Exceed by) = 67.362 − 62.337 = 5.025
4. What number should be added to 1323to get 1257?
a) 20 21
b) 22 21
c) − 20 21
d) − 22 21
Answer: c) −20 21
Explanation: To find the number that should be added, subtract 1323 from 1257.
Required Number = 1257 − 1323
= 897 − 413
= 267 − 287 21 [LCM of 7 and 3 = 7 × 3 = 21]
= − 20 21 or − 2021
5. When Katrina travelled 35 km by car, she found that ?th of her journey was still left. What was the total distance of the whole journey?
a) 9313 km
b) 9323 km
c) 9318 km
d) 9338 km
Answer: a) 9313 km
Explanation: Katrina travelled 35 km.
?th of her journey was still left.
Fraction of her journey travelled = 1 − 58
= 8 − 58 [LCM of 1 and 8 is 8.]
= 38
38th of the total journey = Her journey travelled
⇒ 38 th of the total journey = 35
⇒ Total journey = 35 × 83
⇒ Total journey = 2803
⇒ Total journey = 9313 km
