Question

1: Tanya’s grandfather was 8 times older to her 16 years ago. He would be 3 times her age 8 years from now. Eight years ago, what was the ratio of Tanya’s age to that of her grandfather? [UPSC 2003]

A) 1:2 B) 1: 5 C) 3: 8 D) None of these

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Answer 1

Answer:

Step-by-step explanation:

1:2

Answer 2

QUESTION:-

Tanya’s grandfather was 8 times older to her 16 years ago. He would be 3 times her age 8 years from now. Eight years ago, what was the ratio of Tanya’s age to that of her grandfather?

A) 1:2 B) 1: 5 C) 3: 8 D) None of these

EXPLANATION:-

Let, Tanya's present age be x years

and Tanya's grandfather's age be yyears

Tanya's age 16 years ago =x−16 years

Tanya's grandfather's age =y−16 years

Now,

ATQ

y−16=8(x−16)

⟹y−16=8x−128

y=8x−128+16

y=8x−112    --------(i)

Tanya's age, 8 years from now =x+8

Tanya's grandfather's age, 8 years from now =y+8

A.T.Q,

y+8=3(x+8)

8x−112+8=3(x+8)  -----from (i)

8x−104=3x+24

8x−3x=24+104

5x=128

x=128/5

Put x=128/5 in eq-1

$\bf\;y=\frac{128\times 8}{5}\\\\y=\frac{1024-560}{5}\\\\y=\frac{88}{5}\\\\\\So\;tanya\;grandfather\;age\;8;years\;age=\frac{464}{5}-8\\\\=>\frac{424}{5}$

So ratio=88:424

=>1:53

So OPT-[D] is required answer