Question

Two positive numbers differ by 1280. When the greater number is divided by the smaller number, the quotient is 7 and the remainder is 50. The greater number is:

• A. 1585
• B. 1458
• C. 1558
• D. 1485

Answer 1

Answer:

D. 1485

Given :-

Two positive numbers differ by 1280

When the greater number is divided by the smaller number

The quotient is 7 and the remainder is 50

Concept :- 

Dividend = Quotient $\times$ divisor + remainder

Calculation :-

Let greater number = a and

Smaller number = b

From question,

⇒ a - b = 1280    ....(1)

Again from question, 

⇒ a = 7b + 50    ....(2)

Put the value of a from equation (2) into equation (1)

⇒ 7b + 50 - b = 1280 

⇒ 6b = 1280 - 50 

⇒ 6b = 1230 

⇒ b = $(\frac{1230}{6})$

⇒ b = 205

Put the value of b in equation (1)

⇒ a - 205 = 1280 

⇒ a = 1280 + 205

⇒ a = 1485

⇒ Greater number = 1485 

∴ Greater number is 1485