Q16 of 54 Page 77

The difference between two numbers is 642. When the greater no is divided by the smaller the quotient is 8 and the remainder is 19. Find the number.

Let x be the greater number and y be the smaller number.

Difference = x – y = 642 ……(1)


When the greater number is divided by a smaller number, the quotient is 8 and the remainder is 19.


According to Euclid’s division algorithm


Dividend = Divisor × Quotient + Remainder


x = y×8 + 19


x – 8y = 19 ……(2)


Subtracting equation (1) from equation(2),


7y = 623


y = 89


x – y = 642


x – 89 = 642


x = 731


Therefore, greater number is 731 and smaller number is 89.


More from this chapter

All 54 →
14

The monthly pocket money of Ravi and Sanjeev are in the ratio 5:7. Their expenditures are in the ratio 3:5. If each saves Rs 80 every month find their monthly pocket money.

 15

The denominator of the fraction is 3 more than the numerator. If 5 is added to both the parts, the resulting fraction is equivalent to 4 by 5. Find the fraction.

 17

A man travels 370 km partly by train and partly by car. If he covers 250 km by train and the rest by car it takes him 4 hours but if he travels 130km by train and the rest by the car he takes 18 min. longer. Find the speed of the train and car.

 18

Three times the smallest of three consecutive odd number decreased by 7 equal twice the largest one. Find the number.