IPM Question Paper 2019 | IPM Rohtak Logical Reasoning

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Question 27 : Tanya's grandfather was 8 times older to her 16 years ago. He would be 3 times of her age 8 years from now. What was ratio of ages of Tanya and her grandfather 8 years ago.

1. 11:50
   
2. 11:51
3. 11:53
4. 11:54

Explanatory Answer

Method of solving this IPMAT Question on LR

Let Tanya's present age be x. We know that Tanya's grandfather's age was 8 times her age 16 years ago. 16 years ago Tanya's age was x – 16 and therefore her grandfather's age was 8(x -16). Tanya's grandfather's present age is 8(x – 16) + 16.
8 years from now Tanya's grandfather's age is 3 times Tanya's age.
8(x – 16) + 24 = 3(x + 8)
8x – 128 + 24 = 3x + 24
8x – 3x = 128 ⇒ 5x = 128
x = $\frac{128}{5}$
Tanya's present age is x = $\frac{128}{5}$
Tanya's grandfather's present age is 8($\frac{128}{5}$- 16) + 16 = 8($\frac{48}{5}$) + 16
We need the ratio of Tanya's age to her grandfather's age 8 years ago.
Tanya's age 8 years ago = $\frac{128}{5}$ - 8
Tanya's age 8 years ago = $\frac{128}{5}$ - 8
Tanya's grandfather's age 8 years ago = 8($\frac{48}{5}$) + 8.
Required ratio = $\frac{\frac{128}{5} − 8}{8(\frac{48}{5})+ 8}$ = $\frac{88}{424}$ = $\frac{11}{53}$
The ratio of ages of Tanya and her grandfather 8 years ago is 11 : 53

The question is "Tanya's grandfather was 8 times older to her 16 years ago. He would be 3 times of her age 8 years from now. What was ratio of ages of Tanya and her grandfather 8 years ago."

Hence, the answer is 11:53

Choice C is the correct answer

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