Question

1. The sum of two numbers is 4980. If 13% of the one number is equal to 17% of the other. Find thenumber.​

Answer 1

Answer:

Number 1 = 2822

Number 2 = 2158

Given:

Sum of two numbers = 4980

13% of first number = 17% of second number

Solution:

Let the first number be x and second number be y respectively.

ATQ,

x + y = 4980 .......(1)

13% of x = 17% of y

$\dfrac{13}{100}$ of x = $\dfrac{17}{100}$ of y

Cancelling 100 from both sides , we get:

13x = 17y

x = $\dfrac{17}{13}$y ....(2)

Substituting the value of x from (2) in (1) , we get:

x + y = 4980

$\dfrac{17}{13}$y + y = 4980

Taking LCM , we get:

$\dfrac{17y+13y}{13}$ = 4980

Cross multiplying , we get:

30y = 4980 * 13

Sending 30 to RHS , we get:

y = $\dfrac{4980\times13}{30}$

y = $\dfrac{\cancel{4980}\times 13}{\cancel{30}}$

y = 166 * 13

y = 2158

Substituting the value of y in (2) , we get:

x = $\dfrac{17}{13}\times2158$

x = $\dfrac{17\times\cancel{2158}}{\cancel{13}}$

x = 17*166

x = 2822

Proof:

x + y = 4980

2822 + 2158 = 4980

4980 = 4980

LHS = RHS

Hence Proved

13x = 17y

13 * 2822 = 17 * 2158

36686 = 36686

LHS = RHS

Hence Proved

Therefore, the two numbers are:

x(Number 1) = 2932

y(Number 2) = 2158