Two friends A and B have a total amount of ₹ 1,200. If 7/12th of A's amount is…

Concept — When two amounts share a fixed total and a stated part of one amount is equal to a stated part of the other, rewrite both stated parts in the same form (fractions). An equality of the form p × A = q × B fixes the ratio A : B = q : p, and once that ratio is known the fixed total can be divided in it.

Application

1. Let A and B stand for the two amounts. The total gives A + B = ₹1,200.

2. Write the percentage as a fraction: 25% = 1/4. The stated condition (7/12) × A = 25% of B therefore becomes (7/12)A = (1/4)B.

3. Solve that equality for A: A = (12/7) × (1/4)B = (3/7)B. In ratio form, A : B = 3 : 7.

4. Substitute A = (3/7)B into the total: (3/7)B + B = (10/7)B = ₹1,200.

5. Multiply both sides by 7/10: B = ₹1,200 × 7/10 = ₹840.

Cross-check

• Ratio method: dividing ₹1,200 in the ratio 3 : 7 gives 10 equal parts of ₹120 each, so A = 3 × ₹120 = ₹360 and B = 7 × ₹120 = ₹840.

• Substitution: 7/12 of ₹360 = ₹210, and 25% of ₹840 = ₹210, so the two stated parts are indeed equal.

Therefore B has ₹840.