Question

A man spent 10% of his money , then Rs. 500 ,and and then 5% of remainder .If he has Rs. 95 left , then his original money was ??

Answer 1

Answer

Let the money left before spending the remainder be x.

According to the question,

$\sf \dashrightarrow x - 5\% \: of \: x = 95$

$\sf \dashrightarrow x - \dfrac{5}{100} \times x = 95$

$\sf \dashrightarrow x - \dfrac{5x}{100} = 95$

$\sf \dashrightarrow \dfrac{100x - 5x}{100} = 95$

$\sf \dashrightarrow \dfrac{95x}{100} = 95$

$\sf \dashrightarrow 95x = 95 \times 100$

$\sf \dashrightarrow 95x = 9500$

$\sf \dashrightarrow x = \dfrac{9500}{95}$

$\sf \dashrightarrow x = 100$

Now, let's find the money left with man before spending 500 rupees.

Let the money left with the man before spending 500 be y.

According to the question,

$\sf \dashrightarrow y - 500 = 100$

$\sf \dashrightarrow y = 100 + 500$

$\sf \dashrightarrow y = 600$

Now, let's find the total money he has at beginning.

Let the total money with the boy totally.

Let the money with the boy at beginning be z.

According to the question,

$\sf \dashrightarrow z - 10\% \: of \: z = 600$

$\sf \dashrightarrow z - \dfrac{10}{100} \times z = 600$

$\sf \dashrightarrow z - \dfrac{10z}{100} = 600$

$\sf \dashrightarrow \dfrac{100z - 10z}{100} = 600$

$\sf \dashrightarrow \dfrac{90z}{100} = 600$

$\sf \dashrightarrow 90z = 600 \times 100$

$\sf \dashrightarrow 90z = 60000$

$\sf \dashrightarrow z = \dfrac{60000}{90}$

$\sf \dashrightarrow z = 666.66$

Hence, the man has ₹666.66 with home at beginning.