SSC CGL 2025 Tier-I · 16 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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A bag contains ₹10, ₹5, and ₹2 coins in the ratio 1 : 2 : 3. If the total amount of money in the bag is ₹390, find the number of coins of each kind.

(a)10 coins of ₹10, 20 of ₹5, and 30 of ₹2
(b)15 coins of ₹10, 30 of ₹5, and 45 of ₹2
(c)20 coins of ₹10, 40 of ₹5, and 60 of ₹2
(d)12 coins of ₹10, 24 of ₹5, and 36 of ₹2

Answer

Why

Correct — B. The ratio 1 : 2 : 3 counts coins, so let the counts be x, 2x and 3x.

Value of ₹10 coins = 10 × x = 10x
Value of ₹5 coins = 5 × 2x = 10x
Value of ₹2 coins = 2 × 3x = 6x
Total value = 10x + 10x + 6x = 26x

Solve: 26x = 390, so x = 390 ÷ 26 = 15
Counts = 15, 2 × 15 = 30 and 3 × 15 = 45 → option (b)

Why the others are wrong

(a)
10 coins of ₹10, 20 of ₹5, and 30 of ₹2 — 10, 20 and 30 coins are worth 100 + 100 + 60 = ₹260, not ₹390. The 1 : 2 : 3 pattern is right, but x = 10 is too small.
(c)
20 coins of ₹10, 40 of ₹5, and 60 of ₹2 — 20, 40 and 60 coins are worth 200 + 200 + 120 = ₹520, which overshoots ₹390 by ₹130.
(d)
12 coins of ₹10, 24 of ₹5, and 36 of ₹2 — 12, 24 and 36 coins are worth 120 + 120 + 72 = ₹312, which falls ₹78 short of ₹390.

Concept

When a ratio is given for the number of coins, each kind's value is count × face value. Add the values to get one multiple of x, then solve for x.

Think of one set of 1 ₹10 coin, 2 ₹5 coins and 3 ₹2 coins: it is worth 10 + 10 + 6 = ₹26. The bag holds 390 ÷ 26 = 15 such sets.

Could 1 : 2 : 3 be the ratio of money instead? Then the ₹10 coins would be worth 390 × 1⁄6 = ₹65, which is 6.5 coins. Coins come whole, so the ratio has to be of counts.

Key facts

Value of a group of coins = number of coins × face value.
Counts x, 2x and 3x of ₹10, ₹5 and ₹2 coins are worth 10x + 10x + 6x = 26x.
Check: 15 × 10 + 30 × 5 + 45 × 2 = 150 + 150 + 90 = ₹390.

Study next

Coin problems where the ratio is of values, not countsCoin problems with a total count and a total value (two equations in two unknowns)Dividing a sum of money in a given ratio

Common traps

Reading 1 : 2 : 3 as a ratio of money and splitting ₹390 into ₹65, ₹130 and ₹195.
Picking by pattern: every option keeps 1 : 2 : 3, so only the ₹390 total separates them.

The same frame, a count ratio plus a rupee total with each option listing all three counts, appears at 18 Sep 2025, 09:00, Quant Q.4 (₹5, ₹2 and ₹1 coins in 2 : 3 : 4, totalling ₹200).

A related item at 10 Sep 2024, 09:00, Quant Q.13 (one-rupee, 5-rupee and 10-rupee coins in 3 : 5 : 7, totalling ₹980) asks only for the number of ₹10 coins.

Related PYQs

No directly related past PYQ was found.

Topic: Ratio & Proportion — all 96 SSC CGL questions on it, every solved shift.