Two numbers are in the ratio 5 : 8. If 9 is added to each, the ratio becomes 8 : 11. Find the larger number.

Question

There are 187 fruits in total. The ratio of apples to mangoes is \(2 : 3\), and the rest are oranges. After selling 67 apples, 26 mangoes, and half of the oranges, the ratio of the remaining apples to oranges becomes \(1 : 2\). Determine how many unsold fruits remain.

Answer 1

Step 1: Let the numbers be \(5x\) and \(8x\). Then \(\dfrac{5x+9}{8x+9}=\dfrac{8}{11}\).
Step 2: \(11(5x+9)=8(8x+9)\Rightarrow 55x+99=64x+72\Rightarrow 9x=27\Rightarrow x=3\).
Step 3: Larger number \(= 8x = 24\).

Quick Tip: Introduce a single variable \(x\) for the common ratio unit, then form one equation.

Two numbers are in the ratio 5 : 8. If 9 is added to each, the ratio becomes 8 : 11. Find the larger number.

The Correct Option is B

Solution and Explanation

Top Questions on Ratio and Proportion

Questions Asked in ATMA exam