Initial monthly salaries of Vikas and Rohan were in the ratio 6:7. The individual ratios between their present
and initial mo

2 thoughts on “Initial monthly salaries of Vikas and Rohan were in the ratio 6:7. The individual ratios between their present<br />and initial mo”

1. Answer:

   Rs 24000

   Step-by-step explanation:

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2. 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,

   [tex]\rm :\longmapsto\:4x : 7y = 6 : 7[/tex]

   [tex]\rm :\longmapsto\:\dfrac{4x}{7y} = \dfrac{6}{7} [/tex]

   [tex]\rm :\longmapsto\:\dfrac{4x}{y} = \dfrac{6}{1} [/tex]

   [tex]\bf\implies \:x = \dfrac{3y}{2} – – – (1)[/tex]

   Also,

   According to statement,

   ☆ Sum of their present salary is Rs 62000.

   [tex]\rm :\longmapsto\:5x + 8y = 62000[/tex]

   [tex]\rm :\longmapsto\:5 \times \dfrac{3y}{2} + 8y = 62000[/tex]

   [tex]\rm :\longmapsto\:\dfrac{15y}{2} + 8y = 62000[/tex]

   [tex]\rm :\longmapsto\:\dfrac{15y + 16y}{2}= 62000[/tex]

   [tex]\rm :\longmapsto\:\dfrac{31y}{2}= 62000[/tex]

   [tex]\rm :\longmapsto\:\dfrac{y}{2}= 2000[/tex]

   [tex]\bf\implies \:y = 4000 – – – (2)[/tex]

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

   [tex]\rm :\longmapsto\: \:x = \dfrac{3}{2} \times 2000[/tex]

   [tex]\bf\implies \:x = 3000[/tex]

   Hence,

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

   Additional Information :-

   [tex]\rm :\longmapsto\:If \: \dfrac{a}{b} = \dfrac{c}{d} , \: then[/tex]

   [tex]\green{\boxed{ \bf{ \: \dfrac{a}{c} = \dfrac{b}{d} \: \: \: \: \: \: \: \: \: \: \: \{alternendo \} }}}[/tex]

   [tex]\green{\boxed{ \bf{ \: \dfrac{b}{a} = \dfrac{d}{c} \: \: \: \: \: \: \: \: \: \: \: \{invertendo \} }}}[/tex]

   [tex]\green{\boxed{ \bf{ \: \dfrac{a + b}{b} = \dfrac{c + d}{d} \: \: \: \: \: \: \: \: \: \: \: \{componendo \} }}}[/tex]

   [tex]\green{\boxed{ \bf{ \: \dfrac{a – b}{b} = \dfrac{c – d}{d} \: \: \: \: \: \: \: \: \: \: \: \{dividendo \} }}}[/tex]

   [tex]\green{\boxed{ \bf{ \: \dfrac{a}{b} = \dfrac{c}{d} = \dfrac{a + c}{b + d} \: \: \: \: \: \: \: \: \: \: \: \{addendo \} }}}[/tex]

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