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UPSC Prelims

Mathematics

Theme:

Ratio, Proportion, Partnership and Mixture / अनुपात, समानुपात, साझेदारी और मिश्रण

Q70 2015, Ratio, Proportion, Partnership and Mixture

The monthly incomes of Peter and Paul are in the ratio of 4: 3. Their expenses are in the ratio of 3: 2. If each saves ₹6,000 at the end of the month, their monthly incomes respectively are (in ₹)

पीटर और पॉल की मासिक आय 4:3 के अनुपात में हैं। उनके व्यय 3:2 के अनुपात में हैं। यदि मास के अंत में प्रत्येक व्यक्ति ₹ 6,000 की बचत करता है, तो उनकी मासिक आय (₹ में) क्रमशः क्या है ?

Explanation Please wait..

Given, monthly incomes of Peter and Paul are in the ratio of 4 : 3 and their expenses are in the ratio of 3 : 2.

Let their monthly incomes be ₹ 4x and ₹ 3x and their expenditures be ₹ 3y and ₹ 2y, respectively

Then, 4x - 3y = 6000…(i)

[⸪ Income - Expenditure = Savings]

and 3x - 2y = 6000

From Eqs. (i) and (ii),

4x- 3y = 3x -2 y

= 4x- 3y = 3y - 2y

= x= y

On putting x = y in Eq. (i), we get

4x - 3x = 6000

= x = 6000

Hence, their monthly incomes are ₹(4 x 6000) and ₹(3 x 6000), i.e. ₹24000 and ₹18000

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