Aptitude Solved Problems banker ′s discount

Aptitude Solved Problems

1. The banker ′s discount on a bill due 4 months hence at 15% is Rs. 420. What is the true discount?

Answer: 400

Explanation:
True Discount = ( Banker Discount * 100 ) / [ 100 + ( Time * Rate ) ]
= ( 420 * 100 ) / 100 + [ ( 4 / 12 ) * 15 ]
= ( 420 * 100 ) / 100 + [ ( 1 / 3 ) * 15 ]
= ( 420 * 100 ) / 100 + 5
= ( 420 * 100 ) / 105
= 42000 / 105
= 400

2. How many liters of a 90% of concentrated acid needs to be mixed with a 75% solution of concentrated acid to get a 30 liter solution of 78% concentrated acid?

Answer: 6 litres

Explanation:

Let the concentration of acid be 100.
Let we assign the expected litres of acid as x.
x of 90% mixed with (30 - x) of 75%
(x * 90) + (30 - x) * 75 = 30 * 78
90x + 2250 - 75x = 2340
15x = 2340 - 2250
15x = 90
x = 90 / 15
x = 6 litres

3. A and B can do a piece of work in 18 days; Band C can do it in 24 days A and C can do it in 36 days. In how many days will A, Band C finish it separately?

Answer: 48, 28 (4 / 5), 144

Explanation:

(A + B)′s 1 day′s work = (1 / 18)
(B + C)′s 1 day′s work = (1 / 24)
(A + C)′s 1 day′s work = (1 / 36)
Adding, we get: 2 (A + B + C)′s 1 day′s work = (1 / 18) + (1 / 24) + (1 / 36)
= 9 / 72
2 (A + B + C) =1 / 8
(A + B + C) = 1 / 16
(A +B + C)′s 1 day′s work =1/16
Thus, A, Band C together can finish the work in 16 days.
Now, A′s 1 day′s work = [(A + B + C)′s 1 day′s work] -[(B + C)′s 1 day work:
= (1 / 16) - (1 / 24) = 1 / 48
A alone can finish the work in 48 days.
Similarly, B′s 1 day′s work =(1/16 - 1/36)
= 5 / 144
B alone can finish the work in 144/5 = 28 (4 / 5) days
C′s 1 day′s work =(1 / 16) - (1 / 18)
= 1 / 144
Hence C alone can finish the work in 144 days.
A, B, C can do the work separately in 48, 28 (4 / 5), 144 days respectively.