Question

Initial monthly salaries of Vikas and Rohan were in the ratio 6:7. The individual ratios between their present
and initial monthly salaries are 5:4 and 8:7 respectively. If the sum of their present monthly salaries is 3
62.000, find the initial monthly salary of Vikas.​

Answer 1

Appropriate Question :-

Initial monthly salaries of Vikas and Rohan were in the ratio 6:7. The individual ratios between their present and initial monthly salaries are 5:4 and 8:7 respectively. If the sum of their present monthly salaries is Rs 62, 000, find the initial monthly salary of Vikas.

Solution :-

It is given that

¤ The ratio between the present and initial monthly salary of Vikas is 5 : 4

☆ Let us assume that

• Present salary of Vikas is 5x

• Initial salary of Vikas is 4x.

Also,

It is given that

¤ The ratio between the present and initial monthly salary of Rohan is 8 : 7.

☆ Let us assume that

• Present salary of Rohan is 8y

• Initial salary of Rohan is 7y.

According to statement,

It is given that,

☆ Initial monthly salaries of Vikas and Rohan were in the ratio 6 : 7.

Therefore,

$\rm :\longmapsto\:4x : 7y = 6 : 7$

$\rm :\longmapsto\:\dfrac{4x}{7y} = \dfrac{6}{7}$

$\rm :\longmapsto\:\dfrac{4x}{y} = \dfrac{6}{1}$

$\bf\implies \:x = \dfrac{3y}{2} - - - (1)$

Also,

According to statement,

☆ Sum of their present salary is Rs 62000.

$\rm :\longmapsto\:5x + 8y = 62000$

$\rm :\longmapsto\:5 \times \dfrac{3y}{2} + 8y = 62000$

$\rm :\longmapsto\:\dfrac{15y}{2} + 8y = 62000$

$\rm :\longmapsto\:\dfrac{15y + 16y}{2}= 62000$

$\rm :\longmapsto\:\dfrac{31y}{2}= 62000$

$\rm :\longmapsto\:\dfrac{y}{2}= 2000$

$\bf\implies \:y = 4000 - - - (2)$

☆ On substituting the value of y in equation (1), we get

$\rm :\longmapsto\: \:x = \dfrac{3}{2} \times 2000$

$\bf\implies \:x = 3000$

Hence,

Initial monthly salary of Vikas = 4x = 4 × 3000 = Rs 12000

Additional Information :-

$\rm :\longmapsto\:If \: \dfrac{a}{b} = \dfrac{c}{d} , \: then$

$\green{\boxed{ \bf{ \: \dfrac{a}{c} = \dfrac{b}{d} \: \: \: \: \: \: \: \: \: \: \: \{alternendo \} }}}$

$\green{\boxed{ \bf{ \: \dfrac{b}{a} = \dfrac{d}{c} \: \: \: \: \: \: \: \: \: \: \: \{invertendo \} }}}$

$\green{\boxed{ \bf{ \: \dfrac{a + b}{b} = \dfrac{c + d}{d} \: \: \: \: \: \: \: \: \: \: \: \{componendo \} }}}$

$\green{\boxed{ \bf{ \: \dfrac{a - b}{b} = \dfrac{c - d}{d} \: \: \: \: \: \: \: \: \: \: \: \{dividendo \} }}}$

$\green{\boxed{ \bf{ \: \dfrac{a}{b} = \dfrac{c}{d} = \dfrac{a + c}{b + d} \: \: \: \: \: \: \: \: \: \: \: \{addendo \} }}}$

Answer 2

Answer:

Rs 24000

Step-by-step explanation: