The ratio of expenditure to savings of a woman is 5 ∶ 1. If her income and expenditure are increased by 10% and 20%, respectively, then find the percentage change in her savings.

Question

Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 01 Dec 2022 Shift 3)

Answer 1

Given:

The ratio of expenditure to savings of a woman is 5 ∶ 1.

Her income and expenditure are increased by 10% and 20% respectively.

Concept used:

1. Income = Expenditure + Savings

2. Incremented/Reduced value = Initial value (1 ± change%)

Calculation:

Let her initial expenditure and savings be 5k and k respectively.

Her initial income = 5k + k = 6k

Her final income = 6k × (1 + 10%) = 6.6k

Her final expenditure = 5k × (1 + 20%) = 6k

Her final savings = 6.6k - 6k = 0.6k

Now, % change in savings = \(\frac {k - 0.6k}{k} × 100\%\) = 40%

∴ The percentage change in her savings is 40%.

Shortcut TrickCalculation:

Income = expenditure + saving

⇒ (6 = 5 + 1) × 100

⇒ 600 = 500 + 100

Now, income is increased by 10% and expenditure is increased by 20%.

⇒ 600 × 110% = 500 × 120% + x

⇒ 660 = 600 + x

⇒ x = 60

Percentage change in saving = (100 - 60)/100 = 40%

∴ The correct answer is 40%.

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