Question
The numerator of a fraction is 2 less than its
denominator. If the numerator is decreased by 2 and the denominator is increased by 3, the denominator becomes eight times the numerator. Find the fraction?Solution
Let the required fraction is x/y ATQ: x = y - 2 x - y = -2 ....(i) Also given, y + 3 = 8(x-2) ⇒ y + 3 = 8x – 16 ⇒ 8x – y = 16 + 3 ⇒ 8x – y = 19 …… (ii) Subtracting equation (ii) from (i), we get (x – y) – (8x – y) = – 2 – 19 ⇒ x – y − 8x + y = −21 ⇒ −7x = −21 ⇒ x = 21/7 = 3 Substituting the value of x = 3 in the equation (i) we find y 3 – y = – 2 ⇒ y = 3 + 2 ⇒ y = 5 Therefore, the fraction is 3/5.
The average of four numbers is 150. Two of the numbers are equal (not least), and 50 more than the least number. If the 4th number is twice the least nu...
- The average age of a group of employees is 45 years. When a new employee aged 60 joins, the average increases by 1 year. Find the total age of the group be...
Average marks scored by Vineet in five subjects are 70. The average marks scored by him (excluding his highest and lowest marks) are 50 and lowest marks...
The average weight of 15 oarsmen in a boat is increased by 1.6 kg when one of the crew, who weighs 42 kg, is replaced by a new man. Find the weight of t...
5 positive numbers are written on a piece of paper. Sum of first 3 numbers is 55 and ratio of the 4th and the 5th number is 2:3. If difference between t...
Average age of company A is 22 years and average age of both companies A and B is 14 years. If the ratio of number of employees in company A and B is 3:...
If the average marks of the three batches 32, 45 and 54 student respectively is 50, 42 and 35, then find the approximate average mark of all the students?
A number is such that when it is multiplied by 3, it gives another number which is as much above from 240 as the original number (itself) is below 240. ...
The average number of books sold by Viren in first 5 months is 3000 and in first 6 months is 3800. If the number of books sold by him in 7th ...
A well with 42 m inside diameter is dug 14 m deep. Soil taken out of it has been evenly spread all around it to a width of 21 m to form an embankment. F...
Relevant for Exams:
