BENCHHMARK

Questions

1. To fill a tank, 25 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of bucket is reduced to two fifth of its present ?

2. Meena took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. If she paid Rs. 432 as interest at the end of the loan period, what was the rate of interest?

3. The average weight of 8 person increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?

4. The difference between the circumference and radius of a circle is 37 cm. Then what is the area of the circle in sq.cm?

Answers :
1. 62.5 buckets.
2. 6 %.
3. 85 kg.
4. 154 sq.cm.

1. Explanation:
Let the capacity of 1 bucket = x.
Then, capacity of tank = 25x
New capacity of bucket = 2x / 5
Required no of buckets =25x / ( 2x / 5 )
= ( 25x * 5 ) / 2x
= 125x / 2x
= 62.5
∴ 62.5 buckets will be required.

2. Explanation:
Let Rate = R%
Principal = 1200
Time = R years.
Simple interest = ( Principal * Rate * Time ) / 100
Then, ( 1200 * R * R / 100 ) = 432
12 R2 = 432
R2 = 36
R = 6 %
∴ Rate of interest is 6 %.

3. Explanation:
Total weight increased = ( 8 * 2.5 ) kg
= 20 kg
Weight of new person = ( 65 + 20 ) kg
= 85 kg
∴ The weight of the new person is 85 kg.

4. Explanation:
Let the radius be r cm.
Circumference of circle = 2πr
2πr – r = 37
r ( 2π – 1 ) = 37
r ( 2 * ( 22 / 7 ) – 1)= 37
r (( 44 / 7 ) – 1 ) = 37
r ( 44 – 7 ) / 7 = 37
r ( 37 ) = 37 * 7
r = ( 37 * 7 ) / 37
r = 7 cm
Area of circle = πr2
= ( 22 / 7 ) * 7 * 7
= 154 sq.cm
∴ Area of the circle is 154 sq.cm.