1. If 16 men can reap 80 hectares in 12 days, how many hectares can 36 men reap in 15 days?

Ans:1
In 12 days 16 men can reap 80h
In 1 day 1 man can reap= 80 / (12 x 16)
In 15 days 36 men can reap 80 x 15 x 36 / (12 x 16) =225 hectares

 

2. Arun started a business investing rs 38,000. After 5 months Bakul joined him with a capital of rs 55,000. At the end of the year the total profit was rs 22,000. What is the approximate difference between the share of profits of Arun and Baku!?

Ans:2
Time for which arun invested = 12 months
Time for which bakul invested = 12 -5 = 7 months
Ratio of profit = 38,000 x 12 : 55,000 x 7 = 456 : 385
Arun’s share of profit = 456 / 841 x 22,000 = rs 11,929 (approx.)
Bakul’s share of profit = 385 / 841 x 22,000 = rs 10,071 (approx.)
Difference = 11,929 – 10,071 = rs 1,858
Option (2) is the closest.

 

3. Nitish sold a mango and obtained a profit which is 50% of the selling price of an apple. He sold an apple and he incurred a loss which is equal to half of the selling price of the mango. If the cost price of the apple is twice that of the mango, then what is the ratio of the selling prices of the mango and the apple?

Ans:3
Let the selling prices of the mango and apple be Rs m and Rs a respectively.
Hence the cost price of the mango = m – a/2
And the cost price of the apple = a + m/2
It is given that, a + m/2 = 2(m – a/2)
a + m/2 = 2m – a
=> 2a = 3m/2
=> m : a = 4 : 3

 

4. Two trains 263 meters and 382 meters long respectively are running in the same direction at the speed of 95kmph and 41kmph respectively. In how much time will the first train cross the second one?

Ans:2
Relative speed of trains =95-41=54kmph=54*5/18=15m/s
Time to cross each other=(263+382)/15=43 seconds

 

5. A bus covers a distance of 472 km in 8 hours and a car covers a distance of 312 km. in 6 hours. What is the difference between the speed of the bus and the car?

Ans:5
Speed of bus = 472/8 = 59 km/h
Speed of car = 312/6 = 52 km/h
Difference in speed = 59-52 = 7 km/h

 

6. A person deposited Rs 23500 in a bank which offers 8% simple interest and Rs 19300 in another bank which offers 10% simple interest. Find the total interest obtained in 2 years.

Ans:3
SI from 1st bank = 23500 x 8 x 2/100 = Rs 3760

SI from 2nd bank = 19300 x 10 x 2/100 = Rs 3860

Total interest = 3760 + 3860 = Rs 7620

 

7. The radius of two cylinders of equal height are in the ratio of 1:3. What is the ratio of their volumes?

Ans:2
Ratio of their volumes = (πr12h) / (πr22h) = r12/ (3r1)2 = 1/9

 

8. A circular ring is cut and is bent in the form of a rectangle. The radius of the ring was 21 cm and the sides of the rectangle formed are in the ratio of 7:4. The larger side of rectangle is

Ans:4
Since the same wire is bent, Perimeter of rectangle = circumference of circle
= 2 X 22/7 X 21 = 132 cm
Let the sides of the rectangle be 7L and 4L.
2(7L + 4L) = 132
=> 22L = 132
=> L = 6
Larger side = 7L = 42 cm

 

9. What will be the approximate difference in the simple and compound interest accrued on an amount of Rs 2600 at the rate of 15%, at the end of three years?

Ans:5
CI = 2600[(1 + 0.15]3 – 1]

≈ 2600 x 0.52 = 1352

SI = 2600x15x3/100 = 1170

Difference = 1352 – 1170 = 182

 

10. 20 boys and 32 girls form a group for social work. During their membership drive an equal number of boys and girls also join the group. How many members does the group have now, if the ratio of boys to girls is 3:4?

Ans:5
Let n boys and n girls join the group.
(20+n):(32+n) = 3:4
=> 80+4n = 96+3n
=> n = 16
Strength of the group = 32+20+16+16 = 84

 

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141 thoughts on “Arithmetic”

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