Given below are two statements:
Statement I: a% of b + b% of a = 2(a% of b)
Statement II: A sum of ₹731 is distributed among A, B and C such that A receives 25% more than B and B receives 25% less than C. Then C's share in the amount is ₹272.
In the light of the above statements, choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Both Statement I and Statement II are true
Statement I: a% of b + b% of a = 2(a% of b) Correct. Both percentages come to the same product, so their sum is twice either of them:
a% of b \(=\displaystyle\frac{a}{100}\times b=\frac{ab}{100}\)
b% of a \(=\displaystyle\frac{b}{100}\times a=\frac{ab}{100}\)
Statement II: A sum of ₹731 is distributed among A, B and C such that A receives 25% more than B and B receives 25% less than C. Then C’s share in the amount is ₹272. Correct.
Assuming C’s share to be 100:
B gets 25% less than C: \(B=75\)
A gets 25% more than B: \(A=75+18.75=93.75\)
\(A:B:C=93.75:75:100=15:12:16\), in all \(43\) parts
One part \(=\displaystyle\frac{731}{43}=17\), so C’s share \(=16\times17=\) ₹272