MAT (Stage-2) Mock Test - 23

Let the ages of the mother and her daughter be "X" and "Y" years, respectively.
Thus, [(X + Y) ÷ 2] = 34.5
⇒ (X + Y) = 69 --- (i)
Total age of mother and daughter = 69
Further, Daughter's age = Mother's age/2
Y = X ÷ 2
⇒ X = 2Y --- (ii)
Put the value of X from eq. (ii) in eq. (i).

⇒ 3Y = 69
⇒ Daughter's age = Y = 23 years
Thus, Mother's age = X = 46 years

A scored 720 marks.
Suppose, B scored x marks.
Then, 0.9x = 720
⇒ x = 800
Suppose, C scored y marks.
Then, 1.25y = 800
⇒ y = 640
Suppose, D scored z marks.
Then, 0.8z = 640
⇒ z = 800
So, A scored 720 marks, B scored 800 marks, while C scored 640 marks and D scored 800 marks.
So, % marks scored by D = 800/1000 x 100 = 80%

Let the quantity of milk be 5X litres and that of water be X litres.
Then,
After adding 5 litres of water, ratio becomes 5 : 2.
5X/(X + 5) = 5/2
Or X = 5
⇒ Quantity of milk in the original mixture = 5X litres = 25 litres

Suppose A, B and C take x, y and z days, respectively.
1/x + 1/y = 1/30 … (1)
1/y + 1/z = 1/24 … (2)
1/z + 1/x = 1/20 ... (3)
By solving these equations simultaneously, we get
1/x + 1/y + 1/z = 1/16 ... (4)
By solving (2) and (4), we get x = 48
A, B and C together complete the job in 16 days.
In ten days, 10/16 of the job is completed and 6/16 of the job remains.
∵ x = 48, A completes 1/48 of the job in one day.
∴ Number of days taken by A to complete 6/16 of the job = (6/16) x 48 = 18

Tap X can fill the pool in 36 minutes which means that 1/36^th of the pool will be filled up in a minute.
Tap Y can fill the pool in 48 minutes which means that 1/48^th of the pool will be filled up in a minute.
Given that tap X is open for 27 minutes,
So, (27/36) or (3/4) of the pool will be filled and tap Y has to fill the remaining (1/4)^th of the pool.
Y will fill the entire pool in 48 minutes and for it to fill (1/4)^th of the pool it will take (48/4) = 12 minutes

Length of train = 280 m
Speed = 60 km/hr = 60 × 5/18 = 50/3 m/s
Length of platform = 220 m
Total distance = 280 + 220 = 500 m
Time taken = Distance/Time = 500/50 × 3 = 30 seconds