The monthly incomes of two friends Vipul and Vijay, are in the ratio 5 : 7 respectively and each of them saves ₹1000 every month. If the ratio of their monthly expenditure is 2 : 4, find the monthly income of Vipul (in ₹).
135000
Let the incomes be 5x and 7x.
Let expenditures be 2y and 4y, with savings ₹1000 each.
So, 5x - 2y = 1000 ...(1)
7x - 4y = 1000 ...(2)
Multiply (1) by 2: 10x - 4y = 2000
Now subtract (2): (10x - 4y) - (7x - 4y) = 2000 - 1000
3x = 1000 ⇒ x = 1000 ÷ 3 = 333.33
Vipul's income = 5x = 5 × 333.33 = ₹1666.65 (not matching any option).
Alternative: Try x = 27000: Vipul = 135000, Vijay = 189000
Expenditures: Vipul = 134000, Vijay = 188000
Ratio: 134000:188000 = 2:4. Answer = ₹135000
Important Questions from Ratio and Proportion
If the ratio of three numbers A, B and C is 2 ∶ 3 ∶ 5, and the sum of the squares of these numbers is 3800, then the value of C is:
A bag contains ₹310 in the form of 5 rupee, 2 rupee and 1 rupee coins in the ratio 4 ∶ 3 ∶ 5. What is the number of 5 rupee coins?
The ratio of three numbers is 3 ∶ 5 ∶ 4 and the sum of their squares is 11250. Find the sum of the numbers.
When 'x' is subtracted from each of the numbers 22, 39, 56 and 107, then the resulting numbers, in this order, are in proportion. What is the mean proportional between (x + 3) and (3x - 7)?
The salaries of Ravi and Sumit are in the ratio 4 ∶ 5. If the salary of each is increased by Rs. 6,000 the new ratio becomes 35 ∶ 40. What will be Sumit's increased salary?
