Rs. 720 was divided among A, B, C, D, E. The sum received by them was in ascending order and in arithmetic progression. E received Rs. 40 more than A. How much did B receive?
Rs. 134
Given:-
A+B+C+D+E = Rs. 720
E - A = 40
Concept Used:-
Arithmetic Series -
a, a + d, a + 2d, a + 3d, a + 4d
nth term (Tn) = a + (n -1)d
Calculation:-
Let A receives amount a and the difference between each successive person is d rupees.
AmountE = a + 4d
According to the question,
Amount E = AmountA + 40
⇒ a + 4d - a = 40
⇒ 4d = 40
⇒ d = 10
Also,
Total amount = a + (a + d) + (a + 2d) + (a + 3d) + (a + 4d)
⇒ 720 = 5a + 10d
⇒ 720 = 5a + 100
⇒ a = 124
⇒ AmountB = a + d = 124 + 10 = 134 rupees
Alternate Method
Calculation:
A, B, C, D and E
Since the received amounts are in AP,
the difference between two successive members is constant.
⇒ B – A = C – B = D – C = E – D
We have, E – A = 40,
⇒ B – A = 10, C – B = 10, D – C = 10, E – D = 10,
Let A receives x rupees,
then B, C, D and E will receive,
⇒ x + 10, x + 20, x + 30, x + 40
According to the question,
⇒ x + (x + 10) + (x + 20) + (x + 30) + (x + 40) = 720
⇒ 5x + 100 = 720
⇒ 5x = 620
⇒ x = 124
B will receive = x + 10 = 124 + 10 = 134
∴ B will receive 134 rupees
Important Questions from Integers
Find the number of integers between $1$ and $150$ (inclusive) having $7$ as one of the digits but which are not divisible by $7$.
Integers are listed from 700 to 1000. In how many integers is the sum of the digits 10 ?
Using 2, 2, 3, 3, 3 as digits, how many distinct numbers greater than 30000 can be formed ?
Consider the following statements :
1. The sum of 5 consecutive integers can be 100.
2 The product of three consecutive natural numbers can be equal to their sum.
Which of the above statements is/are correct ?
The difference between a 2-digit number and the number obtained by interchanging the positions of the digits is 54.
Consider the following statements:
1. The sum of the two digits of the number can be determined only if the product of the two digits is known.
2. The difference between the two digits of the number can be determined.
Which of the above statements is/are correct?
