# Simplification

## Simplification

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 Question 1
A man has Rs. 480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
 A 45 B 60 C 75 D 90
Question 1 Explanation:
Let number of notes of each denomination be x. Then x + 5x + 10x = 480 ==> 16x = 480 ==> x = 30. Hence, total number of notes = 3x = 90.
 Question 2
There are two examinations rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is:
 A 20 B 80 C 100 D 200
Question 2 Explanation:
Let the number of students in rooms A and B be x and y respectively. Then, x - 10 = y + 10 x - y = 20 .... (i) and x + 20 = 2(y - 20) x - 2y = -60 .... (ii) Solving (i) and (ii) we get: x = 100 , y = 80. The required answer A = 100.
 Question 3
One-third of Rahul's savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has Rs. 1,50,000 as total savings, how much has he saved in Public Provident Fund ?
 A Rs. 30,000 B Rs. 50,000 C Rs. 60,000 D Rs. 90,000
Question 3 Explanation:
Let savings in N.S.C and P.P.F. be Rs. x and Rs. (150000 - x) respectively. Then, 1/3x = 1/2(150000 - x) =>x/3+x/2= 75000 =>5x/6= 75000 => x =(75000 x 6)/5= 90000 Savings in Public Provident Fund = Rs. (150000 - 90000) = Rs. 60000
 Question 4
In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.40 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for ?
 A 160 B 175 C 180 D 195
Question 4 Explanation:
Suppose the man works overtime for x hours. Now, working hours in 4 weeks = (5 x 8 x 4) = 160. 160 x 2.40 + x x 3.20 = 432 3.20x = 432 - 384 = 48 x = 15. Hence, total hours of work = (160 + 15) = 175.
 Question 5
A man has some hens and cows. If the number of heads be 48 and the number of feet equals 140, then the number of hens will be:
 A 22 B 24 C 26 D 28
Question 5 Explanation:
Let the number of hens be x and the number of cows be y. Then, x + y = 48 .... (i) and 2x + 4y = 140 x + 2y = 70 .... (ii) Solving (i) and (ii) we get: x = 26, y = 22. The required answer = 26
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