Question

In a division sum, the divisor is 18 times the quotient and 9 times the remainder. If the remainder is 26, then the dividend is:
1. 3055
2. 3072
3. 3068
4. 3042

Answer 1

Correct Answer - Option 3 : 3068

Given:

Divisor is 18 times of quotient and 9 times the remainder

Remainder is 26

Formula used:

Dividend = Divisor(D) × Quotient(Q) + Remainder

Calculation:

If D = 18Q, R = 26

Dividend = Divisor(D) × Quotient(Q) + Remainder

⇒ 18Q × Q + 26      ----(1)

If D = 9 × 26, R = 26 

Dividend = Divisor(D) × Quotient(Q) + Remainder

⇒ 9 × 26 × Q + 26      ----(2)

Compare equation (1) and (2)

⇒ 18Q × Q + 26 = 9 × 26 × Q + 26 

⇒ 18Q² = 9 × 26 × Q

⇒ Q = 13

Put the value of Q in equation (2)

Dividend = 9 × 26 × 13 + 26

⇒ 26(117 + 1)

⇒ 3068

∴ The dividend is 3068