**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,

∴

∴ 3 X = 4 Y + 3 ………………. (i)

**Step 2:** By given second condition,

∴

∴ 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 = = 25

**Therefore, the numbers are 25 and 18. **

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