A shopkeeper bought one type of rice at Rs 12 per kg and other type at Rs 16.25 per kg. After mixing both types of rice he fixed the cost of mixture at Rs 14.75 per kg.If the total quantity of the rice be 85 kg ,find the quantity of first type of rice.
Answers
Answer:
30
Step-by-step explanation:
30 kilograms ......
Given :- A shopkeeper bought one type of rice at Rs 12 per kg and other type at Rs 16.25 per kg. The cost of mixture is Rs 14.75 per kg. The total quantity of the rice be 85 kg .
To Find :- The quantity of first type of rice.
Solution :-
Let us assume that, the total quantity of first type of rice is equal to x kg .
Since total quantity of the rice is 85 kg,
→ The total quantity of second type of rice = (85 - x) kg .
So,
→ Cost of first type of rice = Rs.12/kg
→ Total cost of x kg of first type of rice = 12 × x = Rs. 12x
and,
→ Cost of second type of rice = Rs.16.25/kg
→ Total cost of (85 - x) kg of second type of rice = 16.25 × (85 - x) = Rs. 16.25(85 - x)
also,
→ Cost of total quantity of mixture = Rs. 14.75/kg
→ Total cost of 85 kg of mixture = 85 × 14.75 = Rs. 1253.75
then,
→ Total cost of x kg of first type of rice + Total cost of (85 - x) kg of second type of rice = Total cost of 85 kg of mixture
→ 12x + 16.25(85 - x) = 1253.75
→ 12x + 1381.25 - 16.25x = 1253.75
→ 1381.25 - 4.25x = 1253.75
→ 4.25x = 1381.25 - 1253.75
→ 4.25x = 127.5
dividing both sides by 4.25,
→ x = 30 kg (Ans.)
Therefore, the quantity of first type of rice is equal to 30 kg .
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