During the first year, the strength of a school increased by 12%, in the second year it decreased by 12% and in the third year it increased by 10%. At the end of the third year its strength was nearly 10842. What was the strength at the beginning of the first year?

Question

Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 09 Dec 2022 Shift 3)

Answer 1

Given:

During the first year, the strength of school increased by 12%

It decreases by 12% in the second year and in the third year it increase by 10%

Strength at the end of third year is nearly 10842.

Calculation:

Let the initial strength be x.

After 1st year, strength

⇒ x × (1 + 12/100) = x × 1.12

After 2nd year, strength

⇒ x × 1.12 × (1 - 12/100) = x × 1.12 × 0.88

After 3rd year, strength,

⇒ x × 1.12 × 0.88 × (1 + 10/100)

⇒ x × 1.12 × 0.88 × 1.10

We know that after the 3rd year, the strength is 10842.

⇒ x × 1.12 × 0.88 × 1.10 = 10842

⇒ x = 10842 / (1.12 × 0.88 × 1.10)

⇒ x = 10842 / 1.08384

⇒ x ≈ 10000

∴ The strength of the school at the beginning of the first year was nearly 10000.

Shortcut Trick

Now, 6776 unit → 10842,

Then 6250 unit → \(\frac{10842}{6776 } \times 6250\) = 10000