Aptitude - Ratio and Proportion
6.
If a : b = 2 : 3 and b : c = 5 : 7, then a : c =
Answer
ab = 23 and bc = 57
∴ ac =
ab x bc 
= 23 x 57 = 1021
∴ a : c = 10 : 21
Answer :
Option BExplanation :
ab = 23 and bc = 57
∴ ac =
ab x bc = 23 x 57 = 1021∴ a : c = 10 : 21
7.
Which of the following is the lowest ratio ?
Answer
713 = 0.538, 1725 = 0.68, 715 = 0.466, 1523 = 0.652
Clearly, 715 is the smallest.
Answer :
Option CExplanation :
713 = 0.538, 1725 = 0.68, 715 = 0.466, 1523 = 0.652
Clearly, 715 is the smallest.
8.
The mean proportional of 234 and 104 is :
Answer
Mean proportional = √234 x 104 = √13 x 9 x 2 x 2 x 13 x 4
= 13 x 3 x 4 = 156
Answer :
Option DExplanation :
Mean proportional = √234 x 104 = √13 x 9 x 2 x 2 x 13 x 4
= 13 x 3 x 4 = 156
9.
In a mixture of 60 litres, the ratio of milk and water is 2 : 1. If the ratio is to be 1 : 2, the quantity of water to be further added is :
Answer
Quantity of milk = 60 x 23 litres = 40 litres, Water in it = 20 litres
Let the required quantity of water to be added be x litres.
Then, 4020 + x = 12 ⇒ 20 + x = 80 ⇒ x = 60
∴ Water to be added = 60 litres
Answer :
Option DExplanation :
Quantity of milk =
60 x 23 litres = 40 litres, Water in it = 20 litresLet the required quantity of water to be added be x litres.
Then, 4020 + x = 12 ⇒ 20 + x = 80 ⇒ x = 60
∴ Water to be added = 60 litres
10.
The incomes of A and B are in the ratio of 3 : 2 and their expenditures are in the ratio 5 : 3. If each saves 1000, then A's income is :
Answer
Let the incomes of A and B be Rs. 3x and Rs. 2x respectively and let their expenditures be Rs. 5y and Rs. 3y respectively. Then,
3x − 5y = 1000 ... (i)
2x − 3y = 1000 ... (ii)
On solving (i) and (ii), we get x = 2000
∴ A's income = Rs. (3 x 2000) = Rs. 6000
Answer :
Option CExplanation :
Let the incomes of A and B be Rs. 3x and Rs. 2x respectively and let their expenditures be Rs. 5y and Rs. 3y respectively. Then,
3x − 5y = 1000 ... (i)
2x − 3y = 1000 ... (ii)
On solving (i) and (ii), we get x = 2000
∴ A's income = Rs. (3 x 2000) = Rs. 6000
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