Ravi and Sumit's salaries are in the ratio 2:3. After increasing each by Rs. 4000, the ratio becomes 40:57. Find Sumit's original salary.

Problem restatementTwo salaries in ratio 2:3 are each increased by the same amount (Rs. 4000), producing a new ratio 40:57. Determine Sumit's original salary.

Given data

• Let Ravi = 2x, Sumit = 3x
• After increase: (2x + 4000) : (3x + 4000) = 40 : 57

Concept/ApproachTranslate the ratio into an equation via cross-multiplication and solve for x.

Step-by-step calculation57(2x + 4000) = 40(3x + 4000)114x + 228000 = 120x + 1600006x = 68000 ⇒ x = 68000 / 6 = 11333.333…Sumit = 3x = 3 × 11333.333… = Rs. 34,000

Verification/AlternativeNew salaries: Ravi = 2x + 4000 = 22666.666… + 4000 = 26666.666…; Sumit = 34000 + 4000 = 38000; ratio = 26666.666… : 38000 = 40 : 57.

Common pitfallsAttempting to keep x integral; here x is fractional but the salaries after multiplication are valid currency amounts.

Final AnswerRs. 34,000