IPMAT Rohtak 2019 (LR) - 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? | PYQs + Solutions | AfterBoards
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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?

Correct Option: 3
Let Tanya's current age be xx
1616 years ago: \newline y−16=8(x−16)y - 16 = 8(x - 16) where yy is grandfather's current age
88 years from now: \newline y+8=3(x+8)y + 8 = 3(x + 8)
From first equation: \newline y−16=8x−128y - 16 = 8x - 128 \newline y=8x−112y = 8x - 112 ... (1)(1)
From second equation: \newline y+8=3x+24y + 8 = 3x + 24 \newline y=3x+16y = 3x + 16 ... (2)(2)
Equating (1)(1) and (2)(2): \newline 8x−112=3x+168x - 112 = 3x + 16 \newline 5x=1285x = 128 \newline x=1285x = \frac{128}{5}
Substituting in equation (1)(1):
y=8(1285)−112y = 8(\frac{128}{5}) - 112
y=10245−112y = \frac{1024}{5} - 112
y=1024−5605y = \frac{1024-560}{5}
y=4645y = \frac{464}{5}
88 years ago: \newline Tanya's age = 1285−8=128−405=885\frac{128}{5} - 8 = \frac{128-40}{5} = \frac{88}{5}
Grandfather's age = 4645−8=464−405=4245\frac{464}{5} - 8 = \frac{464-40}{5} = \frac{424}{5}
Ratio = 885:4245\frac{88}{5} : \frac{424}{5}
=88:424= 88 : 424 \newline =11:53= 11 : 53
Therefore, the ratio of Tanya's age to her grandfather's age 88 years ago was 11:5311 : 53.

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