Question

A is 25% more than B and B is 40% less than C. If C is 30% more than D, then by what percent is A less than D?​

Answer 1

Given,

A is 25% more than B and B is 40% less than C. If C is 30% more than D.

To find,

by what percent is A less than D.

step 1 : A is 25% more than B.

A = 25% of B + B = 25 × B/100 + B

= B/4 + B = 5B/4

⇒A/B = 5/4 .........(1)

step 2 : B is 40% less than C.

B = C - 40% of C = C - 40 × C/100

= C - 2C/5 = 3C/5

⇒B/C = 3/5 .........(2)

step 3 : C is 30% more than D.

C = 30% of D + D = 30 × D/100 + D

= 3D/10 + D = 13D/10

⇒C/D = 13/10 ........(3)

multiplying equations (1) , (2) and (3) we get,

A/B × B/C × C/D = 5/4 × 3/5 × 13/10 = 39/40

⇒A/D = 39/40

so, A = 39 and D = 40

then percent of A is less than D = (D - A)/D × 100

= (40 - 39)/40 × 100

= 100/40

= 2.5 %

Therefore A is 2.5% less than D.