Out of two numbers, 40% of the greater number is equal to 60% of the smaller. If the sum of the numbers is 150, then the greater number is :

Let the greater and smaller number is a and b respectively
According to the question,

Case (i)
a × $$\frac{40}{100}$$ = b × $$\frac{60}{100}$$
2a = 3b
a = $$\frac{3}{2}$$b ..... (i)

Case (ii)
a + b = 150 ..... (ii)
From equation (i) and (ii)
$$\frac{3}{2}$$b + b = 150
5b = 300
b = 60
Value of b = 60 put in equation (i)
a = $$\frac{3}{2}$$ × 60 = 90
Hence, greater number = 90