We begin with a simple example. Sum of two numbers is 74. One of the numbers is 10 more than the other. What are the numbers?
We do not know either of the two numbers, and we have to find them. We are given two conditions.
(i) One of the numbers is 10 more than the other.
(ii) Their sum is 74.
If the smaller number is taken to be x, the larger number is 10 more than x, i.e., x + 10. The other condition says that the sum of these two numbers x and x + 10 is 74.
This means that x + (x + 10) = 74.
or 2x + 10 = 74
Transposing 10 to RHS, 2x = 74 – 10
or 2x = 64
Dividing both sides by 2, x = 32. This is one number.
The other number is x + 10 = 32 + 10 = 42
The desired numbers are 32 and 42. (Their sum is indeed 74 as given and also one number is 10 more than the other.)
Baichung’s father is 26 years younger than Baichung’s grandfather and 29 years older than Baichung. The sum of the ages of all the three is 135 years. What is the age of each one of them?
Lakshmi is a cashier in a bank. She has currency notes of denominations Rs 100, Rs 50 and Rs 10, respectively. The ratio of the number of these notes is 2:3:5. The total cash with Lakshmi is Rs 4, 00,000. How many notes of each denomination does she have?
Three consecutive integers are such that when they are taken in increasing order and multiplied by 2, 3 and 4 respectively, they add up to 74. Find these numbers.