Question

Ritu thought of a number. One-seventh of the number exceeds one-eighth of the number by 12. What is the number Ritu thought of?​

Answer 1

✬ Number = 672 ✬

Explanation:

Given:

• One seventh of a number exceeds one eighth of the number by 12.

To Find:

• What is the number ?

Solution: Let the number be x. Therefore,

➟ 1/7th part of x = 1/7 × x = x/7

➟ 1/8th part of x = 1/8 × x = x/8

A/q

• Ones seventh part exceeds one eighth part by 12

• 1/7th part = 1/8th part + 12

Hence, our equation will be

$\implies{\rm }$ x/7 = x/8 + 12

$\implies{\rm }$ x/7 = (x + 96)/8

$\implies{\rm }$ 8 × x = 7 × (x + 96)

$\implies{\rm }$ 8x = 7x + 672

$\implies{\rm }$ 8x – 7x = 672

$\implies{\rm }$ x = 672

Hence, the number she thought was 672.

[ Verification ]

• Seventh part = 672/7 = 96

• Eighth part = 672/8 = 84

• Difference = 96 – 84 = 12

$\large\bold{\texttt {Verified }}$

Answer 2

$\sf \underline{Given} :$

• Ritu thought of a number. One-seventh of the number exceeds one-eighth of the number by 12.

$\sf \underline{To \: Find} :$

• What is the number Ritu thought of?

$\sf \underline{Solution} :$

Supposed the number is A :

$\underline{ \boldsymbol{According \: to \: the \: question \: \: }} :$

$\sf : \implies \: \frac{1}{7}th \: part \: of \: x \: = \frac{x}{7} \\ \\ \\ \sf : \implies \: \frac{1}{8}th \: part \: of \: x \: = \frac{x}{8}$

Ones seventh part exceeds one eighth part by 12

$\sf : \implies \: \frac{x}{7} = \frac{x}{8} + 12 \\ \\ \\ \sf : \implies \: \frac{x}{7} = \frac{x + 96}{8} \\ \\ \\ \sf : \implies \: 8x = 7x + 672 \\ \\ \\ \sf : \implies \: 8x - 7x = 672 \\ \\ \\ \sf : \implies \: x = 672$

the number Ritu thought of 672