Exercise: Simplification
Questions for: Simplification
To fill a tank, 25 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to two-fifth of its present ?
Answer: C
Let the capacity of 1 bucket = x.
Then, the capacity of tank = 25x.
| New capacity of bucket = | 2 | x |
| 5 |
 Required number of buckets = |
25x |
| (2x/5) |
| = |  25x |
x | 5 |  |
| 2x |
| = | 125 |
| 2 |
= 62.5
Eight people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire cost of the car, then the share of each of the remaining persons increased by:
Answer: A
| Original share of 1 person = | 1 |
| 8 |
| New share of 1 person = | 1 |
| 7 |
| Increase = | |
1 | - | 1 | |
= | 1 |
| 7 | 8 | 56 |
| Required fraction = |
(1/56) | = | |
1 | x | 8 | |
= | 1 |
| (1/8) | 56 | 1 | 7 |
A fires 5 shots to B's 3 but A kills only once in 3 shots while B kills once in 2 shots. When B has missed 27 times, A has killed:
Answer: A
Let the total number of shots be x. Then,
| Shots fired by A = | 5 | x |
| 8 |
| Shots fired by B = | 3 | x |
| 8 |
| Killing shots by A = | 1 | of | 5 | x | = | 5 | x |
| 3 | 8 | 24 |
| Shots missed by B = | 1 | of | 3 | x | = | 3 | x |
| 2 | 8 | 16 |
| |
3x | = 27 or x = | |
27 x 16 | |
= 144. |
| 16 | 3 |
| Birds killed by A = | 5x | = | |
5 | x 144 | |
= 30. |
| 24 | 24 |
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 ?
Answer: C
Let savings in N.S.C and P.P.F. be Rs. x and Rs. (150000 - x) respectively. Then,
| 1 | x = | 1 | (150000 - x) |
| 3 | 2 |
 |
x | + | x | = 75000 |
| 3 | 2 |
|
5x | = 75000 |
| 6 |
| x = |
75000 x 6 | = 90000 |
| 5 |
Savings in Public Provident Fund = Rs. (150000 - 90000) = Rs. 60000
A sum of Rs. 1360 has been divided among A, B and C such that A gets 
of what B gets and B gets 
of what C gets. B's share is:
of what B gets and B gets of what C gets. B's share is:
Answer: C
Let C's share = Rs. x
| Then, B's share = Rs. | x | , A's share = Rs. | |
2 | x | x | |
= Rs. | x |
| 4 | 3 | 4 | 6 |
|
x | + | x | + x = 1360 |
| 6 | 4 |
|
17x | = 1360 |
| 12 |
| x = |
1360 x 12 | = Rs. 960 |
| 17 |
| Hence, B's share = Rs. | |
960 | |
= Rs. 240. |
| 4 |
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