1.) If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 50, what is the compound interest on the same at the same rate and for the same time?
Sum = (50*100)/(2*5) = Rs. 500
Amount = 500(1+5/100)^2 = 551.25
interest =551.25- 500 = Rs 51.5
2.) 5 years ago, the average age of P, Q and R was 25 year; 7 years ago the average age of Q & R was 20 years. Find the present age of P?
Present age of P+Q+R = 25*3+ 5*3= 90 year
Present age of Q+R= 20*2 + 7 *2 = 54 year
present age of P = 90-54 = 36 year.
3.) A dealer mixes tea costing Rs. 6.92 per kg with tea costing Rs. 7.77 per kg and sells the mixture at Rs. 8.80 per kg and earns a profit of 17 .5 % on his sale price. In what proportion does he mix them?
Let us first find the cost price (C.P.) of the mixture. If S.P. is Rs. 100, profit is 17.5
Therefore C.P. = Rs. (100 - 17.5) = Rs. 82.5
If S.P. is Rs. 8.80, C.P. is (82.5× 8.80)/ 100 = Rs. 7.26
C.P. of the mixture per kg = Rs. 7.26
2nd difference = Profit by selling 1 kg. of 2nd kind @ Rs. 7.26
= Rs. 7.77 – Rs. 7.26 = 51 paise
1st difference = Rs. 7.26 – Rs. 6.92 = 34 paise
We have to mix the two kinds in such a ratio that the amount of profit in the first case
must balance the amount of loss in the second case.
Hence, the required ratio = (2nd diff) : (1st diff.) = 51 : 34 = 3 : 2.
4.) A sum of Rs. 46875 was lent out at simple interest and at the end of 1 year 8 months the total amount was Rs. 50000. Find the rate of interest percent per annum.
Interest= Rs. 50,000 - 46875 = Rs. 3125
1 year 8 month = 5/3 year
so 3125= (46875*r*5)/(3*100)
on solving this r = 4%
5.) In what ratio will the total wages of the workers of a factory be increased or decreased if there be a reduction in the number of workers in the ratio 15 : 11 and an increment in their wages in the ratio 22 : 25.?
Let x be the original number of workers and Rs. y the (average) wages per workers.
Then the total wages before changes = Rs. xy.
After reduction, the number of workers = (11 x)/15
After increment, the (average) wages per workers = Rs.(25 y)/22
The total wages after changes = (11x/15) × (25y/22) =5xy/6
Thus, the total wages of workers get decreased from Rs. xy to Rs. 5xy/6
Hence, the required ratio in which the total wages decrease is xy:5xy/6 = 6:5
6.) Seats for Mathematics, Physics and Biology in a school are in the ratio 5 : 7 : 8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats?
math : Physics : bio = 5:7:8
After increment 5*140/100 : 7*150/100 : 8*175/100
14:21:28= 2:3:4
7.) A, B and C jointly thought of engaging themselves in a business venture. It was agreed that A would invest Rs. 6500 for 6 months, B, Rs. 8400 for 5 months and C, Rs. 10,000 for 3 months. A wants to be the working member for which, he was to receive 5% of the profits. The profit earned was Rs. 7400. Calculate the share of B in the profit.
Remain profit for A, B & C
7400*95/100= 7030
A:B:C= 6500*6 : 8400*5 : 10,000*3 = 39:42:30
Share of B= 7030*42/111 = Rs. 2660
8.) Daily earnings of two persons are in the ratio 4:5 and their daily expenses are in the ratio 7:9, If each saves Rs. 50 per day, their daily incomes in Rs. are
let earning= 4x : 5x;
expences= 7y:9y
saving = income - expences
4x-7y= 5x-9y = 50
on solving both eqn. x=100
So Daily income are Rs. 400 and Rs. 500
9.) Aman begin a business with rupees 2100 and join afterwards by Kamal with rupees 3600, After how many months Kamal join if the profit at the end of the year are divided equally.
let Kamal work for y months.
2100* 12 = 3600 * y ;
y = 7 months .
so duration after kamal join = 12-7 = 5 months.
10. A shopkeeper Purchase a chair mark at rupees 800, at two successive discount of 10% and 15% respectively. He spent Rs. 25 on transportation and sold the chair for Rs. 800.Find his gain/loss percent?
marked Price =800
Seling price after discount= 800*90/100*85/100 = 612
Total price including transportation = 612 + 25 = 637
selling it to 800 there would be gain
so gain % = (800 - 637)/637 *100 = 25 % approx
- A) 50.75
- B) 52
- C) 51.25
- D) 54
- E) None of these.
Sum = (50*100)/(2*5) = Rs. 500
Amount = 500(1+5/100)^2 = 551.25
interest =551.25- 500 = Rs 51.5
2.) 5 years ago, the average age of P, Q and R was 25 year; 7 years ago the average age of Q & R was 20 years. Find the present age of P?
- A) 30
- B) 35
- C) 36
- D) 40
- E) 90
Present age of P+Q+R = 25*3+ 5*3= 90 year
Present age of Q+R= 20*2 + 7 *2 = 54 year
present age of P = 90-54 = 36 year.
3.) A dealer mixes tea costing Rs. 6.92 per kg with tea costing Rs. 7.77 per kg and sells the mixture at Rs. 8.80 per kg and earns a profit of 17 .5 % on his sale price. In what proportion does he mix them?
- A) 17:13
- B) 2:3
- C) 3:2
- D) 13:17
- E) None of these.
Let us first find the cost price (C.P.) of the mixture. If S.P. is Rs. 100, profit is 17.5
Therefore C.P. = Rs. (100 - 17.5) = Rs. 82.5
If S.P. is Rs. 8.80, C.P. is (82.5× 8.80)/ 100 = Rs. 7.26
C.P. of the mixture per kg = Rs. 7.26
2nd difference = Profit by selling 1 kg. of 2nd kind @ Rs. 7.26
= Rs. 7.77 – Rs. 7.26 = 51 paise
1st difference = Rs. 7.26 – Rs. 6.92 = 34 paise
We have to mix the two kinds in such a ratio that the amount of profit in the first case
must balance the amount of loss in the second case.
Hence, the required ratio = (2nd diff) : (1st diff.) = 51 : 34 = 3 : 2.
4.) A sum of Rs. 46875 was lent out at simple interest and at the end of 1 year 8 months the total amount was Rs. 50000. Find the rate of interest percent per annum.
- A) 2.5%
- B) 5%
- C) 4%
- D) 6%
- E) None of these.
Interest= Rs. 50,000 - 46875 = Rs. 3125
1 year 8 month = 5/3 year
so 3125= (46875*r*5)/(3*100)
on solving this r = 4%
5.) In what ratio will the total wages of the workers of a factory be increased or decreased if there be a reduction in the number of workers in the ratio 15 : 11 and an increment in their wages in the ratio 22 : 25.?
- A) 5:6
- B) 6:5
- C) 25:36
- D) 125:33
- E) None of these.
Let x be the original number of workers and Rs. y the (average) wages per workers.
Then the total wages before changes = Rs. xy.
After reduction, the number of workers = (11 x)/15
After increment, the (average) wages per workers = Rs.(25 y)/22
The total wages after changes = (11x/15) × (25y/22) =5xy/6
Thus, the total wages of workers get decreased from Rs. xy to Rs. 5xy/6
Hence, the required ratio in which the total wages decrease is xy:5xy/6 = 6:5
6.) Seats for Mathematics, Physics and Biology in a school are in the ratio 5 : 7 : 8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats?
- A) 6:9:13
- B) 7:8: 19
- C) 2:3:4
- D) None of these
- E) Can’t be determined.
math : Physics : bio = 5:7:8
After increment 5*140/100 : 7*150/100 : 8*175/100
14:21:28= 2:3:4
7.) A, B and C jointly thought of engaging themselves in a business venture. It was agreed that A would invest Rs. 6500 for 6 months, B, Rs. 8400 for 5 months and C, Rs. 10,000 for 3 months. A wants to be the working member for which, he was to receive 5% of the profits. The profit earned was Rs. 7400. Calculate the share of B in the profit.
- A) 2000
- B) 2500
- C) 2660
- D) 2700
- E) None of these.
Remain profit for A, B & C
7400*95/100= 7030
A:B:C= 6500*6 : 8400*5 : 10,000*3 = 39:42:30
Share of B= 7030*42/111 = Rs. 2660
8.) Daily earnings of two persons are in the ratio 4:5 and their daily expenses are in the ratio 7:9, If each saves Rs. 50 per day, their daily incomes in Rs. are
- A) 40, 50
- B) 50, 40
- C) 400, 500
- D) None of these
- E) Can’t be Determined
let earning= 4x : 5x;
expences= 7y:9y
saving = income - expences
4x-7y= 5x-9y = 50
on solving both eqn. x=100
So Daily income are Rs. 400 and Rs. 500
9.) Aman begin a business with rupees 2100 and join afterwards by Kamal with rupees 3600, After how many months Kamal join if the profit at the end of the year are divided equally.
- A) 4 months
- B) 5 months
- C) 6 months
- D) 7 months
- E) 9 months
let Kamal work for y months.
2100* 12 = 3600 * y ;
y = 7 months .
so duration after kamal join = 12-7 = 5 months.
10. A shopkeeper Purchase a chair mark at rupees 800, at two successive discount of 10% and 15% respectively. He spent Rs. 25 on transportation and sold the chair for Rs. 800.Find his gain/loss percent?
- A) Gain 25%
- B) Loss 25 %
- C) Gain 11.11 %
- D) Loss 11.11 %
- E) No gain no Loss
marked Price =800
Seling price after discount= 800*90/100*85/100 = 612
Total price including transportation = 612 + 25 = 637
selling it to 800 there would be gain
so gain % = (800 - 637)/637 *100 = 25 % approx