Question

Ratna has ₹200 more than three times the amount Rafik has. If ₹ 300 from the amount with Ratna are given to Rafik, amount with Ratna will be 7/4 times the amount with Rafik. Find the initial amount with Rafik. To find the initial amount, complete the following activity.
Solution: The amount with Ratna is ₹ 200 more than three times the amount with Rafik.
Let the initial amount with Rafik be ₹ x. ∴ Ratna has ₹ .....
∴ ₹ 300 from Ratna are given to Rafik.
∴ Remaining amount with Ratna is .....
∴ Now Rafik has ₹ ( x + 300)
Now the amount with Ratna is 7/4 times the amount with Rafik
∴ Amount with Ratna / Amount with Rafik = ...../.....
∴ (3x - 100) / (x + 300) = ..... / .....
∴ 4 ..... = 7 .....
∴ 12x -400 = 7x + 2100
∴ 12x - 7x = .....
∴ 5x = .....
∴ x = .....
∴ Rafik initially has ₹ ..... with him.

Answer 1

Solution: The amount with Ratna is ₹ 200 more than three times the amount with Rafik.

Let the initial amount with Rafik be ₹ x.
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∴ Ratna has ₹ $\mathit{\underline{200 + 3x}}$

∴ ₹ 300 from Ratna are given to Rafik.

∴ Remaining amount with Ratna is ₹ $\mathit{\underline{ - 300 + 200 + 3x}}$

∴ Now Rafik has ₹ ( x + 300)


Now the amount with Ratna is 7/4 times the amount with Rafik

∴ Amount with Ratna / Amount with Rafik = $\mathit{\underline{\frac{7/4*(x + 300)}{x + 3}}}$

∴ (3x - 100) / (x + 300) = $\mathit{\underline{7/4}}$

∴ 4 (3x - 100) = 7 (x + 300)

∴ 12x - 400 = 7x + 2100

∴ 12x - 7x = 2100 + 400

∴ 5x = 2500

∴ x = 2500/5 = 500

∴ Rafik initially has ₹ 500 with him.

Answer 2

Ratna has ₹200 more than three times the amount Rafik has. If ₹ 300 from the amount with Ratna are given to Rafik, amount with Ratna will be 7/4 times the amount with Rafik. Find the initial amount with Rafik. To find the initial amount, complete the following activity.

Solution: The amount with Ratna is ₹ 200 more than three times the amount with Rafik.

Let the amount with Rafik be Rs x.

Then amount with Ratna = 3x + 200

According to the 2nd condition we have :

(3x + 200 - 300) = (7/4)(x + 300)

or, 4(3x + 200 - 300) = 7(x + 300)

or, 12x - 400 = 7x +2100

or, 12x - 7x = 2100 + 400

or, 5x = 2500

or, x = 500(Ans)

Therefore, initial amount with Rafik was Rs 500 and with Ratna was Rs 1700.