Aptitude Solved Problems

Aptitude Solved Problems..!

Bright Zoom Maths,

 Question  :1

The ratio of the number of boys and girls in a school is 7 : 8. If the percentage increase in the number of boys and girls be 10% and 30% respectively, what will be the new ratio?

Answer: 77 : 104

Explanation:

Originally, let the number of boys and girls in the school be 7x and 8x respectively
Their increased number is 
(110% of 7x) and (130% of 8x)
=> ( 110 / 100 ) * 7x and
 ( 130 / 100 ) * 8x
=> ( 11 / 10 ) * 7x and ( 13 / 10 ) * 8x
=> ( 77 / 10 ) * x and ( 104 / 10 ) * x
The required ratio
 = ( 77x / 10 ) : ( 104x / 10 )
= 77x : 104x
= 77 : 104
∴ Required ratio = 77 : 104

Question  :2
2. A 200m long train is running at 54 Kmph. how much time it will take to cross a platform of 115m long?

Answer: 21 sec

Explanation:

Total distance = Length of the train + Length of the platform
= 200 m + 115 m
= 315 m
Speed = 54 km / hr
To convert km / hr in to m / s
x km / hr = x * ( 5 / 18 ) m / s
Speed = 54 * ( 5 / 18 ) m / s
= 3 * 5
= 15 m / s
Distance = Speed * Time
315 m = 15 m / s * Time
( 315 / 15 ) = Time

∴ Time = 21 sec


Question  :3

A boat moves upstream at the rate of 1 km in 20 minutes and down stream 1 km in 10 minutes. The speed of the current is :

Answer: 1.5 km / hr

Explanation:

Rate upstream 
= ( 1 / ( 20 / 60 )) km / hr
= 1 * ( 60 / 20 )
= 1 * 3
= 3 km / hr

Rate dowmstream 
= ( 1 / ( 10 / 60 )) km / hr
= 1 * ( 60 / 10 )
= 1 * 6
= 6 km / hr

Rate of the current
 = ( 1 / 2 ) * ( Rate dowmstream - Rate upstream )
= ( 1 / 2 ) * ( 6 - 3 )
= ( 1 / 2 ) * 3
= 1.5 km / hr

∴ Rate of the current = 1.5 km / hr

Question  :4

The banker′s discount on a bill due 4 months hence at 6 % is Rs. 459. What is the true discount?

Answer: Rs. 450

Explanation:
Banker′s discount = Rs. 459
Rate = 6 %
Time = 4 months
= ( 4 / 12 ) year
True discount 
= ( Banker′s discount * 100 ) / ( 100 + ( Rate * Time ))
= ( 459 * 100 ) / ( 100 + ( 6 * ( 4 / 12 )))
= 45900 / ( 100 + 2 )
= 45900 / 102
= Rs. 450

∴ True discount = Rs. 450

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