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Question

The ratio of the incomes of A and B last year was 4 ∶ 3, respectively. The ratios of their individual incomes of the last year and the present year are 3 ∶ 4 and 5 ∶ 6, respectively. If their total income for the present year is Rs. 8.04 lakh, then the income of B last year was∶

This question was previously asked in
SSC CGL 2018 (Tier 2) Statistics Previous Year Paper (22-feb-2018)
The correct answer is

Rs. 2.7 lakh

Step 1 — Last year's incomes:

Let A and B's last-year incomes be \(4x\) and \(3x\) (lakh).

Step 2 — Present-year incomes:

A's last : present = 3 : 4, so A now earns \(4x \times \tfrac{4}{3} = \tfrac{16x}{3}\). B's last : present = 5 : 6, so B now earns \(3x \times \tfrac{6}{5} = \tfrac{18x}{5}\).

Step 3 — Use the total:

\[\frac{16x}{3} + \frac{18x}{5} = 8.04 \implies \frac{134x}{15} = 8.04\]

\[x = \frac{8.04 \times 15}{134} = 0.9\]

Therefore B's income last year \(= 3x = \mathbf{Rs.\ 2.7\ lakh}\).

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Similar Questions

  1. A family income is Rs. 35,000 in a month. The family spends the income on various expenditures, viz., food, health, education, entertainment, and rent. After incurring all the expenditures, 8% is saved every month. The expenditure on health is 50% more than that of food. While food is three times of the expenditure on entertainment, the expenditure on health is half of the expenditure on education. The expenditure on rent is one-third of the combined expenditure on food, health and education. How much expenditure (in Rs.) is incurred on education?

  2. Two numbers are in the ratio 2 : 3. If 5 is subtracted from the first number and six is added to the second number, then the ratio becomes 5 : 12. What would the ratio become when eight is added to each number?

  3. The ratio of number of cans of orange, pineapple and mixed fruit juices kept in a store is 8 : 9 : 15. If the store sells 25%, 33.33% and 20% of orange, pineapple and mixed fruit juices cans respectively, then what is the ratio of number of cans of these juices in the remaining stock?

  4. The ratio of monthly incomes of A and B is 4 ∶ 5 and that of their monthly expenditures is 3 ∶ 8. If the income of A is equal to the expenditure of B, then what is the ratio of savings of A and B?

  5. The train ticket fare from places A to B in 2 nd class AC and 3 rd class AC is Rs. 2,500 and Rs. 2,000, respectively. If the fares of 2 nd class AC and 3 rd class AC are increased by 20% and 10%, respectively, then find the ratio of the new fares of 2 nd class AC and 3 rd class AC.

  6. The ratio of the monthly incomes of A and B is 11 : 13 and the ratio of their expenditures is 9 : 11. If both of them manage to save Rs. 4,000 per month, then find the difference in their incomes (in Rs.)

  7. In an examination, the number of students who passed and the number of students who failed were in the ratio 25 ∶ 4. If one more student had appeared and passed and the number of failed students was 3 less than earlier, the ratio of passed students to failed students would have become 22 ∶ 3. What is the difference between the number of students who, initially, passed the examination and the number of students who failed the examination?

  8. If (5a – 3b) : (4a – 2b) = 2 : 3, then a : b is equal to:

  9. The ratio of boys and girls in a school is 27 : 23. If the difference between the number of boys and girls is 200, then find the number of boys.

  10. The sum of weights of A and B is 80 kg. 50% of A's weight is \(\frac 5 6\)  times the weights of B. Find the difference between their weights.


Important Questions from Simple Ratios

  1. If the value of \(\frac{{p - q}}{q} = \frac{4}{3}\)  .find p : q

  2. Half of the villagers of a certain village have their own houses. One-fifth of the villagers cultivate paddy. One-third of the villagers are literate. Four-fifth of the villagers are under 25 years of age. Which one of the following statements is certainly correct ?

  3. The two numbers are in the ratio of 9 ∶ 7 and the difference between of these two number is 6000. What is the sum of the two numbers?

  4. A certain number is added to each of a pair of numbers which are in the ratio 4 ∶ 5. The sum of the resulting numbers is 39 and their ratio (taken in the same order as mentioned above) is 6 ∶ 7. What is the number added?

  5. If (p + q) ∶ (q + r) ∶ (r + p) = 5 ∶ 6 ∶ 7 and p + q + r = 18, find the value of p ∶ q ∶ r

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