Arithmetic

Ratio, Proportion & Variation

Medium

Two numbers are in the ratio 3:5. If 3 is subtracted from the first number and 3 is added to the second number, the ratio becomes 1:3. The sum of the numbers is?

✅ Correct Option: 4

Two numbers are in the ratio 3:5.

Let the first number be $3x$ and the second number be $5x$ , where $x$ is a common multiplier.

After the changes:

First number becomes $3x - 3$
Second number becomes $5x + 3$
New ratio is 1:3

This gives us:

$\frac{3x - 3}{5x + 3} = \frac{1}{3}$

$3(3x - 3) = 1(5x + 3)$

$9x - 9 = 5x + 3$

$9x - 5x = 3 + 9$

$4x = 12$

$x = 3$

The actual numbers are:

First number $= 3x = 3 \times 3 = 9$

Second number $= 5x = 5 \times 3 = 15$

Sum $= 9 + 15 = 24$

Therefore, the sum of the numbers is 24.

2022: 24 Aug Shift 1

If A : B = 4 : 5, B : C = 4 : 15 and C : D = 5 : 16 Than find the ratio between A and D :

2023: 1 June Shift 1

A sum of Rs. 1250 is divided among A, B and C such that A gets $\frac{2}{9}$ of B's share and C gets $\frac{3}{4}$ of A's share. Find the shares of A, B and C (in Rs.).

2026: 22 May Shift 2

What must be added to each term of the ratio 7 : 11 to make it equal to 3 : 4?

2026: 31 May Shift 2

The mean proportional between 0.08 and 0.18 is?

2024

The sum of three numbers is $136$ . If the ratio between the first number and the second number is $2 : 3$ and that between the second and the third number is $5 : 3$ , then the first number is:

2022: 8 Aug Shift 1

Ratio between age of P and Q is 5 : 7. If 2 years ago Q's age was 2 years more than the age of P after 4 years, then find their total age

Two numbers are in the ratio 3:5. If 3 is subtracted from the first number and 3 is added to the second number, the ratio becomes 1:3. The sum of the numbers is?

Solution

Related questions:

Keyboard Shortcuts

CUET General Test Past Year Questions (Topic-Wise)