During a division, Pranjal mistakenly took as the dividend a number that was 10% more than the original dividend. He also mistakenly took as the divisor a number that was 25% more than the original divisor. If the correct quotient of the original division problem was 25 and the remainder was 0, what was the quotient that Pranjal obtained, assuming his calculations had no error?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 22.
Let's denote the original dividend as D, the original divisor as V, and the correct quotient of the original division as Q.
Given that
Pranjal mistakenly took the dividend as 110% of the original dividend, which is 1.10D.
Pranjal mistakenly took the divisor as 125% of the original divisor, which is 1.25V.
Now, let's calculate the quotient Q' that Pranjal obtained:
Q' = (Dividend taken by Pranjal) / (Divisor taken by Pranjal)
Q' = (1.10D) /(1.25V)
We know that the correct quotient (Q) is 25, and there is no remainder (remainder = 0). This means:
Q = D / V
Now, let's solve for D in terms of V:
D = Q × V
Now, substitute this expression for D into the formula for Q':
Q' = (1.10D)/(1.25V)
⇒ Q' = (1.10 × Q × V)/(1.25V)
Now, simplify the expression:
⇒ Q' = (1.10 × Q) / 1.25
Now, plug in the value of Q, which is 25:
⇒ Q' = (1.10 × 25)/1.25
⇒ Q' = (27.5)/1.25
⇒ Q' = 22
Hence, the quotient that Pranjal obtained, assuming his calculations had no error, is 22.