Q29 of 35 Page 3


If three times the larger of the two numbers is divided by the smaller one, weget 4 as quotient and 3 as the remainder. Also if seven times the smallernumber is divided by the larger one, we get 5 as quotient and 1 as remainder.Find the numbers.


Let the larger number be x and smaller one be y.
We know that
Dividend = (Divisor × Quotient) + Remainder
3x = 4y + 3
3x – 4y – 3 = 0 … (ii)
7y = 5x + 1
5x – 7y + 1 = 0 … (iii)
Solving (ii) and (iii) by cross – multiplication, we get
⇒
x = 25 and y = 18.

More from this chapter

All 35 →
27
A man walks a certain distance at a certain speed. Had he walked (1/2) km/hrfaster, he would have taken 3hours longer. Find the distance.
 28
By selling a table and a chair for 1896, a trader gains 25% on the tableand 10% on the chair. If he sells them for 1770, he makes a profit of 10%on the table and 25% on the chair. Find the cost price of each.
 30
The sum of the numerator and denominator of a fraction is 4 more than twice thenumerator. If the numerator and denominator are increased by 3, they are in theratio 2:3. Determine the fraction.
 31
A two-digit number is 4 more than 6 times the sum of its digits. If 18 issubtracted from the number, the digits are reversed. Find the number.