Question

The expenses on rice, fish and oil of a family are in the ratio 12 : 17 : 13. The price of these articles have increased by 20%, 30% and 50% respectively. The total expenses of family on these articles are increased by:
(a) $14 \dfrac{1}{3}$
(b) $7 \dfrac{1}{3}$
(c ) $56 \dfrac{1}{3}$
(d) $33 \dfrac{1}{3}$

Answer 1

Hint: First we need to assume a common factor for the given ratios. Then we need to increase the prices according to the percentage given.

Complete step-by-step answer:
Given, The expenses on rice, fish and oil of a family are in the ratio 12 : 17 : 13. The price of these articles have increased by 20%, 30% and 50% respectively.
Let the previous expenses on rice be Rs. 120
Let the previous expenses on fish be Rs. 170
Let the previous expenses on oil be Rs. 130
Increment of price on rice is 20%
Thus the increased expense on rice is
$\dfrac{20}{100} \times 120 =24$
Increment of price on fish is 30%
Thus the in Increment on fish is
 $\dfrac{30}{100} \times 170 =51$
Increment of price on oil is 50%
Thus the increased expense on oil is
$\dfrac{50}{100} \times 130 =65$
Required percentage increment is $\dfrac{24+51+65}{120+170+130} \times 100 = \dfrac{140}{420} \times 100$
By calculating we get the percentage increment as $33 \dfrac{1}{3}$
Thus the answer is option d.


Note: In such a type of question we can take the common value of the ratio as per our requirement to simplify the calculation but the ratio must be the same as mentioned in question.