Question

The monthly salaries of A and B are in the ratio 3:5. If A and B get an increase of 5% and 10% of their existing salaries respectively, what will be the new ratio?​

Answer 1

Answer:

The new salaries of A and B will be in ratio 63 : 110.

Step-by-step explanation:

Method I -

Let the salaries be :

• A's salary = 3y
• B's salary = 5y

★ Increased salary of A :

$\longrightarrow{ \: \sf{3y + ( 5\% \: of \: 3y) \dfrac{}{}}}$

$\longrightarrow{ \: \sf{3y + \bigg( \dfrac{5}{100} \times 3y \bigg)}}$

$\longrightarrow{ \: \sf{3y + \dfrac{3y}{20}}}$

$\longrightarrow{ \: \sf{\dfrac{60y + 3y}{20}}}$

$\longrightarrow{ \: \sf{\dfrac{63y}{20}}}$

★ B's increased salary :

$\longrightarrow{ \: \sf{5y + ( 10\% \: of \: 5y)}}$

$\longrightarrow{ \: \sf{5y + \bigg( \dfrac{10}{100} \times 5y \bigg)}}$

$\longrightarrow{ \: \sf{5y + \dfrac{5y}{10}}}$

$\longrightarrow{ \: \sf{\dfrac{50y+5y}{10}}}$

$\longrightarrow{ \: \sf{\dfrac{55y}{10}}}$

★ New Ratio =

$\bf{A's\:new\:salary : B's\:new\:salary}$

$\sf{\longrightarrow} \: \dfrac{63y}{20 \: } : \: {\dfrac{55y}{10}}$

$\sf{\longrightarrow} \: \dfrac{63y}{20} \: : \dfrac{110y}{20}$

$\sf{\longrightarrow} \:63 \: : \: 110$

Therefore, the new salaries of A and B will be in ratio 63 : 110.

__________________

Method II -

Let the salaries of,

• A be Rs. 300
• B be Rs. 500

A gets 5% raise and B gets 10% raise.

★ A's new salary =

$\sf{\longrightarrow} \:300 + (5\% \: of \: 300)$

$\sf{\longrightarrow} \:300 + 15$

$\sf{\longrightarrow} \:315$

★ B's new salary =

$\sf{\longrightarrow} \:500 + (10\% \: of \: 500)$

$\sf{\longrightarrow} \:500 + 50$

$\sf{\longrightarrow} \:550$

★ Their new salary ratio =

$\sf{\longrightarrow} \:315 \: : \: 550$

$\sf{\longrightarrow} \:63 \: : \: 110$

Therefore, the new salaries of A and B will be in ratio 63 : 110.

Answer 2

Given :-

The monthly salaries of A and B are in the ratio 3:5. If A and B get an increase of 5% and 10% of their existing salaries respectively,

To Find :-

what will be the new ratio?

Solution :-

Let their salaries be 3a and 5a

For A

He got an increase of 5%

Increase in salary = 5% of 3a

Increase in salary = 5/100 × 3a

Increase in salary = 0.05 × 3a

Increase in salary = Rs. 0.15a

New Salary = Old salary + Increase in salary

New Salary = 3a + 0.15a

New Salary = (3 + 0.15)a

New Salary = 3.15a

For B

He got an increase of 10%

Increase in salary = 10% of 5a

Increase in salary = 10/100 × 5a

Increase in salary = 0.1 × 5a

Increase in salary = 0.5a

New Salary = Old salary + Increase in salary

New Salary = 5a + 0.5a

New Salary = (5 + 0.5)a

New Salary = 5.5a

Ratio = 3.15a/5.5a

Ratio = 3.15/5.5

Ratio = 3150/5500

Ratio = 315/550

Ratio = 63/110

Ratio = 63 : 110