1. A and B started a business with initial investments in the ratio 14 : 15 and their annual profits were in the ratio 7 : 6. If A invested the money for 10 months, and B invested his money for x months, then the value of x is
Let the investment of A and B are 14a and 15a
so.(14a*10)/(15a*x)=7/6
x=8 month
2. If a sum of money placed at compound interest, compounded annually, doubles itself in 5 years, then the same amount of money will be 8 times of itself in.
in 5 years 2 times Let in n years 8 times=2^3 times
n=5X3=15 years
3. A reduction of 10% in the price of wheat enables a man to buy 50 grams of wheat more for a rupee. How much wheat could originally he had for a rupee?
New price of 50 gm=100*10/100=10 paise
so, new Price of 500 gm=100 paise
The wheat for 1Rs originally=500*90/100=450 grams
4. The ratio of the first and second class fares between two railway stations is 4 : 1 and that of the number of passengers traveling by first and second classes is 1 : 40. If on a day Rs. 1100 are collected as total fare, the amount collected form the first class passengers is
Let the first class fare is 4x and second class fare is x Rs.Let the no of passengers travelling by first class is y and by second class is 40y.
total fare of first class=4xy
total fare of second class=40xy
4xy+40xy=1100
xy=25
so amount collected by first class passengers=4xy=4x25=100
5. Water is flowing at the rate of 5 km/h through a pipe of diameter 14 cm into a rectangular tank which is 50 m long. 44 m wide. The time taken, in hours, for the rise in the level of water in the tank to be 7 cm is
Volume of water
= 5000cm × 4400cm × 7cm = 5000 × 4400 × 7
Volume of water in one hour = 22/7X7X7X5000X100
Required Time== 5000 × 4400 × 7/(22/7X7X7X5000X100)
=2hours
6. A person took a loan of Rs. 6000 for 3 years, at 5% per annum compound interest. He repaid Rs. 2100 in each of the first 2 years. The amount he should pay at the end of 3rd year to clear all his debts is
Amount for first year=6000X105/100=6300
After repaid 2100 the rest amount=6300-2100=4200
Amount for 2nd year=4200X105/100=4410
after repaid 2100 the rest amount=4410-2100=2310
amount for 3rd year=2310x105/100=2425.5
7. A boat travels 24 km upstream in 6 hours and 20 km downstream in 4 hours. Then the speed of boat in still water and the speed of water current are respectively
The speed downstream = 20/4=5kmph
The speed upstream = 24/6=4kmph
The speed of boat in still water = (5+4)/2=4.5kmph
The speed of current = (5-4)/2=0.5
The speed of boat and water current are 4.5 km/hr. and 0.5 km/hr. respectively.
8. A man buys three houses, the second one at twice the price of the first and the third one at twice the price of the second. He manages to sell the first and the second both at a profit of 20% but incurs a loss of 10% over selling the third. Overall, he has profit or loss%.
According to question
CP1=100,CP2=200 and CP3=400
SO SP1=120,SP2=220 and SP3=360
Total CP=100+200+400=700
total SP=120+220+360=720
Profit=720-700=20
Profit%=20X100/700=2.85%
9. A man buys two chairs for a total cost of Rs. 900. By selling one for 4/5 of its cost and the other for 5/4 of its cost, he makes a profit of Rs. 90 on the whole transaction. The cost of the lower priced chair is
Let CP of first chair =x
CP of 2nd chair=900-x
so,SP of 1st chair=4x/5
and SP of 2nd chair=(900-X)5/4
Profit=SP-Cp
90=4x/5+(900-X)5/4-900
X=300
1st chair CP=300 and 2nd chair=600
10. A boy can swim in still water at a speed of 10 km/hr. If the speed of the current would have been 5 km/hr, then the boy could swim 60 km.
Speed downstream = 10 + 5 = 15 km/hr
Speed upstream = 10 – 5 = 5 km/hr
Time taken to swim 60 km downstream = 60/15=4hour
But time taken to swim 60 km up steam = = 60/5=12 hour
- (a) 6
- (b) 7
- (c) 8
- (d) 9
- (e) none of these
Let the investment of A and B are 14a and 15a
so.(14a*10)/(15a*x)=7/6
x=8 month
2. If a sum of money placed at compound interest, compounded annually, doubles itself in 5 years, then the same amount of money will be 8 times of itself in.
- (a) 25 years
- (b) 20 years
- (c) 15 years
- (d) 10 years
- (e) none of these
in 5 years 2 times Let in n years 8 times=2^3 times
n=5X3=15 years
3. A reduction of 10% in the price of wheat enables a man to buy 50 grams of wheat more for a rupee. How much wheat could originally he had for a rupee?
- (a) 400 grams
- (b) 500 grams
- (c) 450 grams
- (d) 350 grams
- (e) none of these
New price of 50 gm=100*10/100=10 paise
so, new Price of 500 gm=100 paise
The wheat for 1Rs originally=500*90/100=450 grams
4. The ratio of the first and second class fares between two railway stations is 4 : 1 and that of the number of passengers traveling by first and second classes is 1 : 40. If on a day Rs. 1100 are collected as total fare, the amount collected form the first class passengers is
- (a) Rs.315
- (b) Rs.315
- (c) Rs.137.50
- (d) Rs.100
- (e) none of these
Let the first class fare is 4x and second class fare is x Rs.Let the no of passengers travelling by first class is y and by second class is 40y.
total fare of first class=4xy
total fare of second class=40xy
4xy+40xy=1100
xy=25
so amount collected by first class passengers=4xy=4x25=100
5. Water is flowing at the rate of 5 km/h through a pipe of diameter 14 cm into a rectangular tank which is 50 m long. 44 m wide. The time taken, in hours, for the rise in the level of water in the tank to be 7 cm is
- (a)2
- (b)1.5
- (c)6
- (d)2.5
- (e)none of these
Volume of water
= 5000cm × 4400cm × 7cm = 5000 × 4400 × 7
Volume of water in one hour = 22/7X7X7X5000X100
Required Time== 5000 × 4400 × 7/(22/7X7X7X5000X100)
=2hours
6. A person took a loan of Rs. 6000 for 3 years, at 5% per annum compound interest. He repaid Rs. 2100 in each of the first 2 years. The amount he should pay at the end of 3rd year to clear all his debts is
- (a) Rs.2425.50
- (b) Rs.2552.50
- (c) Rs.2635.50
- (d) Rs. 2745.50
- (e) none of these
Amount for first year=6000X105/100=6300
After repaid 2100 the rest amount=6300-2100=4200
Amount for 2nd year=4200X105/100=4410
after repaid 2100 the rest amount=4410-2100=2310
amount for 3rd year=2310x105/100=2425.5
7. A boat travels 24 km upstream in 6 hours and 20 km downstream in 4 hours. Then the speed of boat in still water and the speed of water current are respectively
- (a) 4 kmph and 3 kmph
- (b) 4.5 kmph and 0.5 kmph
- (c) 4 kmph and 2 kmph
- (d) 5 kmph and 2 kmph
- (e) none of these
The speed downstream = 20/4=5kmph
The speed upstream = 24/6=4kmph
The speed of boat in still water = (5+4)/2=4.5kmph
The speed of current = (5-4)/2=0.5
The speed of boat and water current are 4.5 km/hr. and 0.5 km/hr. respectively.
- (a)got a profit less than 3%
- (b) incurred a loss of 3%
- (c)got a profit more than 3%
- (d) incurred a loss less than 3%
- (e) none of these
According to question
CP1=100,CP2=200 and CP3=400
SO SP1=120,SP2=220 and SP3=360
Total CP=100+200+400=700
total SP=120+220+360=720
Profit=720-700=20
Profit%=20X100/700=2.85%
9. A man buys two chairs for a total cost of Rs. 900. By selling one for 4/5 of its cost and the other for 5/4 of its cost, he makes a profit of Rs. 90 on the whole transaction. The cost of the lower priced chair is
- (a) Rs. 360
- (b) Rs. 400
- (c) Rs. 420
- (d) Rs. 300
- (e)none of these
Let CP of first chair =x
CP of 2nd chair=900-x
so,SP of 1st chair=4x/5
and SP of 2nd chair=(900-X)5/4
Profit=SP-Cp
90=4x/5+(900-X)5/4-900
X=300
1st chair CP=300 and 2nd chair=600
10. A boy can swim in still water at a speed of 10 km/hr. If the speed of the current would have been 5 km/hr, then the boy could swim 60 km.
- (a) upstream in 4 hours
- (b) downstream in 12 hours
- (c) upstream in 6 hours
- (d) downstream in 4 hours
- (e) none of these
Speed downstream = 10 + 5 = 15 km/hr
Speed upstream = 10 – 5 = 5 km/hr
Time taken to swim 60 km downstream = 60/15=4hour
But time taken to swim 60 km up steam = = 60/5=12 hour