Question

Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is
A. 2:3
B. 3:4
C. 4:5
D. 5:6

Answer 1

Hint: We are asked to find the ratio, so we’ll convert the two given numbers in fraction form so that we can take their ratio afterwards. Assuming the first number to be 100% make the increments in the first two numbers and then take their ratio.

Complete step-by-step answer:
Let the third number be x
Then, first number = 120% of x
=\[\dfrac{{120x}}{{100}}\]
=\[\dfrac{{6x}}{5}\]
Second number = 150% of x
=\[\dfrac{{150x}}{{100}}\]
=\[\dfrac{{3x}}{{100}}\]
Now, ratio of first two numbers = \[\dfrac{{6x}}{5}:\dfrac{x}{2}\]
=\[12x:15x\]
=\[4:5\]
∴ The correct option is ‘c’.

Note: For solving questions like these, you must have the knowledge of how the percentages are taken, how increments and decrements can be done in them and more importantly how % can be converted into fraction.