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Arjun and Prateek have toffees with them in the ratio 7 ∶ 9. If Arjun is given 32 more toffees, the ratio of the number of toffees with them gets reversed. How many toffees would have been given to Arjun to make the ratio 10 ∶ 7?

Arjun and Prateek have toffees with them in the ratio 7 ∶ 9. If Arjun is given 32 more toffees, the ratio of the number of toffees with them gets reversed. How many toffees would have been given to Arjun to make the ratio 10 ∶ 7? Correct Answer 41

Given:

Arjun and Prateek have toffees with them in the ratio 7 ∶ 9.

If Arjun is given 32 more toffees, the ratio of the number of toffees with them gets reversed

Formula:

If the ratio of A and B is a ∶ b, assume A = ak and B = bk

where k is a constant.

Calculation:

Let the number of toffees with Arjun and Prateek be 7x and 9x respectively.

According to question

(7x + 32)/9x = 9/7

⇒ 49x + 224 = 81x

⇒ x = 7

Toffees with Arjun = 7x = 7 × 7 = 49

Toffees with Prateek = 9x = 9 × 7 = 63

Let the number of toffees given to Arjun be k.

So, (49 + k)/63 = 10/7

⇒ 49 + k = 90

⇒ k = 41

∴ The number of toffees is given to Arjun is 41

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