Question

Rahul's age was 2 times the Mohit's age. If 6 is subtracted from Mohit's age and 4 years added to Rahul's age, then Rahul's a will be 4 times than Mohit's age. Find their ages before 2 years.​

Answer 1

Step-by-step explanation:

Given:-

• Rahul's age was 2 times the Mohit's age. If 6 is subtracted from Mohit's age and 4 years added to Rahul's age, then Rahul's a will be 4 times than Mohit's age.

To Find:-

• Their ages before 2 years.

Solution:-

$\sf \: Suppose \: two \: years \: before \: \\ \sf \: Mohit's \: age \: was \red{ \bigstar\: x \: years \bigstar} \: and \\ \sf \: suppose \: Rahul's \: age \: was \: \red{ \bigstar 2x \: years \bigstar} \\ \\ \rm \: \clubs New\: age \: of \: Mohit \\ \leadsto \bf \: x - 6 \: years \\ \\ \rm \: \clubs \: New \: age \: of \: Rahul \\ \leadsto \bf \: 2x + 4 \: years \\ \\ \bf \: ACQ \\ \therefore \: \tt4(x - 6) = 2x + 4 \\ \dashrightarrow \tt4x - 24 = 2x + 4 \\ \dashrightarrow \tt4x - 2x = 4 + 24 \\ \dashrightarrow \tt2x = 28 \\ \dashrightarrow \tt \: x = 14 \\ \dashrightarrow \tt \green{x = 14} \\ \\ \\ {\huge{♦}} \: \bf \: Present \: age \: of \: rahul = \\ \twoheadrightarrow\sf \: 2x \: years \\ \twoheadrightarrow \sf \: 2 \times 14 \: years \\ \twoheadrightarrow \bf 28 \: years \\ \\ {\huge{♦}} \: \bf \: Present \: age \: of \: Mohit = \\ \twoheadrightarrow \sf \: x \: years \\ \twoheadrightarrow \bf \: 14 \: years \\ \\ \color{maroon}\boxed{\begin{array}{c} \: \sf \: Two \: years \: ago \\ \\ \sf \: Mohit's \: age = 14 - 2 \\ \color{maroon} \dashrightarrow \bf \: 12 \: years \\ \\ \sf \: Rahul's \: age = 28 - 2 \\ \dashrightarrow \bf \: 26 \: years \end{array}}$