If three times the greater of two numbers is divided by the smaller

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Q) If three times the greater of two numbers is divided by the smaller one, we get 4 as the quotient and 3 as the remainder. Also, if seven times the smaller number is divided by greater one, we get 5 as the quotient and 1 as the remainder. Find the numbers.

Ans:

STEP BY STEP SOLUTION

Let’s consider the two numbers be X and Y, where X > Y

Step 1: By given first condition, $\frac{3 \times}{Y} = 4 \frac{3}{Y}$

∴ $\frac{3 \times}{Y} = \frac{4 Y + 3}{Y}$

∴ 3 X = 4 Y + 3 ………………. (i)

Step 2: By given second condition, $\frac{7 Y}{\times} = 5 \frac{1}{\times}$

∴ $\frac{7 Y}{\times} = \frac{5 \times + 1}{\times}$

∴ 7 Y = 5 X + 1

∴ 5 X = 7 Y – 1 ………………. (ii)

Step 3: Multiply equation (i) by 5 and compare with 3 times of equation (ii), we get:

5 (3 X) – 3 (5 X) = 5 (4 Y + 3) – 3 (7 Y – 1)

∴ 15 X – 15 X = 20 Y + 15 – 21 Y + 3

∴ 0 = – Y + 18

∴ Y = 18

Step 4: Next, by substituting value of Y in equation (i), we get:

3 X = 4 Y + 3

∴ 3 X = 4 (18) + 3 = 75

∴ X = $\frac{75}{3}$ = 25

Therefore, the numbers are 25 and 18.

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