SSC CGL 2025 Tier-I · 15 September 2025, Shift 1 · Quantitative Aptitude · Question 2 of 100

We transcribed this text from the pictures on a candidate's response sheet for this shift; the answer is the key SSC colour-marked on that sheet. Solution last reviewed 13 September 2026.

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Simplify:(7⁄5 ÷ 14⁄15) × (10⁄7 ÷ 5⁄3)

(a)9⁄7
(b)5⁄7
(c)6⁄7
(d)8⁄7

Answer

Why

Correct — A. Dividing by a fraction means multiplying by its reciprocal.

First bracket: 7⁄5 ÷ 14⁄15 = 7⁄5 × 15⁄14
= 105⁄70 = 3⁄2
Second bracket: 10⁄7 ÷ 5⁄3 = 10⁄7 × 3⁄5
= 30⁄35 = 6⁄7

Multiply the brackets: 3⁄2 × 6⁄7 = 18⁄14
= 9⁄7 → option (a)

Why the others are wrong

(b)
5⁄7 — 5⁄7 is smaller than 6⁄7, but the answer is 6⁄7 multiplied by 3⁄2, a number greater than 1. That product must exceed 6⁄7.
(c)
6⁄7 — 6⁄7 is the second bracket on its own. It still has to be multiplied by the first bracket, 3⁄2, which gives 9⁄7.
(d)
8⁄7 — 8⁄7 would need the first bracket to be 8⁄7 ÷ 6⁄7 = 4⁄3. The first bracket is 7⁄5 × 15⁄14 = 3⁄2.

Concept

Division by a fraction is multiplication by its reciprocal: a⁄b ÷ c⁄d = a⁄b × d⁄c. Flip only the divisor, never the number being divided.

Cancel before multiplying to keep the numbers small. In 7⁄5 × 15⁄14, the 7 goes into 14 and the 5 into 15, leaving 3⁄2. In 10⁄7 × 3⁄5, the 5 goes into 10, leaving 2 × 3⁄7 = 6⁄7.

Once both divisions are flipped, the expression is one product: 7⁄5 × 15⁄14 × 10⁄7 × 3⁄5. The numerators multiply to 3150 and the denominators to 2450, and 3150⁄2450 reduces to 9⁄7.

Key facts

a⁄b ÷ c⁄d = a⁄b × d⁄c.
Multiplying by a fraction greater than 1 makes a number larger: 3⁄2 × 6⁄7 = 9⁄7, more than 6⁄7.
9⁄7 ≈ 1.286.

Study next

BODMAS when ÷ and × appear without brackets, worked left to rightMixed numbers converted to improper fractions before dividingCancelling common factors across numerators and denominators

Common traps

Flipping the first fraction instead of the divisor: 5⁄7 × 14⁄15 = 2⁄3, not 3⁄2.
Stopping after one bracket: the second bracket's value, 6⁄7, is itself an option.

Division by a fraction inside a bracket also decides 17 Sep 2024, 09:00, Quant Q.13: 1⁄6 ÷ 1⁄9 = 3⁄2, times 2⁄3 is 1, so the expression is 1 × 18 + 5 = 23.

Related PYQs

No directly related past PYQ was found.

Topic: Basic algebraic identities of School Algebra & Elementary surds — all 182 SSC CGL questions on it, every solved shift.