Simplification with Explanation

Q8. In a training center if all the students are accommodated according to 7 students per bench, there would be space left for 5 students. However, if 6 students are accommodated per bench, one more bench will be required. How many students are there in the training center?

Q9. The cost of 3 jackets and 4 sweaters is Rs. 6200 and 4 jackets and 3 sweaters cost Rs. 6400. What is the cost of buying 12 jackets?

Answer- Option C

Explanation-

Let the price of jacket and sweater be Rs. x and Rs. y
3x + 4y = 6200 ...(i)
4x + 3y = 6400 ...(ii)
On solving these two equations, x = Rs. 1000
The price of 12 jackets = Rs. 12000

Q10. A software development company decided to take his employees for a picnic and planned to spend Rs. 96 on eatable items. Due to some reason, four employees did not turn up. As a result, the remaining one had to contribute Rs. 4 each extra. How many employees had attended the picnic?

Answer- Option A

Explanation-

Let the number of employees be x. Then,

96 x - 4

-

96 x

= 4

x² - 4x - 96 = 0
(x - 12)(x + 8) = 0
x = 12

Q11. There are two lifts A and B in an apartment that run at a rate of 63 floors per minute and 57 floors per minute respectively. Madhav gets on a lift B at the 11th floor and rides up. While at the same time, Raghav gets on a lift A at the 51st floor and rides down. Find the floor at which they will meet each other?

Answer- Option D

Explanation-

Let they meet after x minutes.
Then, 11 + 57x = 51 - 63x ⇔ x =

1 3

Number of floors covered by Madhav in (1/3) min =

1 3

x57 = 19

So, they will meet at 11 + 19 = 30th floor.

Q12. After distributing the chocolates equally among 25 kids, 8 chocolates remain. Had the number of children been 28, 22 chocolates would have been left after equally distributing. Find the total number of chocolates?

Answer- Option C

Explanation-

Let each kid gets x chocolates. Then, the number of chocolates = (25x + 8)
(25x + 8) - 22 is divisible by 28.
(25x - 14) is divisible by 28.
28x - (3x + 14) is divisible by 28.
(3x + 14) is divisible by 28. ⇔ x = 14
Total number of chocolates = (25*14 + 8) = 358

Q13. Rajesh owes Rs. X and gives a Rs. 50 note in payment. He receives the following change: 14 ten-paisa coins, 3X fifty-paisa coins, and 4X five-paisa coins. What is the value of X?

Answer- Option A

Explanation-

X + 3X * 0.50 + 14 * 0.10 + 4X * 0.05 = 50
2.7X = 48.60
X = 18

Q14. If every 3 out of 4 readymade suits need alterations in the sleeves and every 2 out of 5 need alterations in the collar. How many alterations are required in 20 suits?

Answer- Option D

Explanation-

Number of alterations required in 1 suit =

3 4

+

2 5

=

23 20

Number of alterations needed in 20 suits =

23 20

x 20 = 23