When price of sugar is increased by 35% a person gets 14 kg less sugar in Rs 160. Find the new price of sugar per kg?a)Rs 31kgb)Rs 4 kgc)Rs 5 kgd)Rs 6 kgCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

Given:
- Increase in price of sugar = 35%
- Reduction in quantity of sugar for Rs. 160 = 14 kg

To find: New price of sugar per kg

Assumption:
Let the original price of sugar be Rs. x per kg.

Calculation:

1. Calculation of original quantity of sugar for Rs. 160:
- Let the original quantity of sugar for Rs. 160 be y kg.
- Then, according to the question, we can form the following equation:

y/x = 160/x - (35/100) * (160/x)
=> y/x = 1 - 0.35
=> y/x = 0.65

- Solving for y, we get:
y = 0.65x

2. Calculation of new price of sugar:
- Let the new price of sugar be Rs. p per kg.
- According to the question, we know that the person is getting 14 kg less sugar for Rs. 160 at the new price.
- So, we can form the following equation:

(160/p) - 14 = 160/x
=> 160/p = 160/x + 14
=> p = (160/x + 14) * (1/160)

- Substituting the value of y/x from step 1, we get:
p = (160/x + 14) * (1/160)
=> p = (160/(0.65x) + 14) * (1/160)
=> p = (246 + 14) / (160 * 0.65)
=> p = 4

Therefore, the new price of sugar per kg is Rs. 4.

Hence, the correct answer is option (b).

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