MAT (Stage-2) Mock Test - 17

Let Bob and Smith take x and y days, respectively to finish the job.
∴ 1/x + 1/y = 1/8 {∴ both can together finish the work in 8 days}
In 3 days, 3/8 of the work is done. Smith completes the remaining 5/8 of the given work in 15 days.
Hence, Smith can complete the given work alone in:
(8/5) x 15 = 24 days
⇒ y = 24 and x = 12
∴  Bob alone takes 12 days to finish the job.

1^st case:
S.P. = Rs. 200
Profit = Rs. 25
∴C.P. = S.P. - Profit
= 200 - 25 = Rs. 175
2^nd case:
C.P. = Rs. 175
Profit = Rs. 50
∴ He should sell the candies at the price of 175 + 50 = Rs. 225

1^st case:
Loss = Rs. 400
2^nd case:
If S.P. = Rs. 4800
Profit = Rs. 800
∴ C.P. = S.P. - Profit
C.P. = 4800 - 800 = Rs. 4000
∴ S.P. = C.P. - Loss = (4000 - 400) = Rs. 3600

According to the question,
25% of 80 is 25/100×80 = 20 kg
So, the wife's weight is 80 - 20 = 60 kg
Son's weight = 10% of mother's weight + mother's weight
 Son's weight = (10/100×60) + 60
= 6 + 60 = 66 kg
Weight of the son is 66 kg.

According to the question,
Ratio = 3 : 2
First term = 3
Second term = 2
Total length = 2 m and 50 cm = 200 + 50 = 250 cm
Length of the longer piece = First term/Sum of terms × Total length
= 3/(3+2) × 250
= 3/5 × 250 = 150 cm
= 1 m and 50 cm

SP = Rs. 240
Loss = 4%
SP = CP - 4% of CP
∴ 0.96CP = Rs. 240
⇒ CP = Rs. 250
To make profit of 10%
New SP = CP + 10% of CP
New SP = Rs. (250 x 110)/100 = Rs. 250 x 1.1 = Rs. 275

Let the cost price of the packet of pens be Rs. 100.
So, cost of 1 pen = Rs. 10
SP of 1 pen = Rs. 10 + 20% of 10 = Rs. 12
SP of 12 pens = 12 x 12 = Rs. 144
Profit percentage = (144-100)/100×100
= (44)/100×100 = 44%