**Find solutions for all the questions at the end of each set:**

### Set A

1.Amit took a bus from home to market, that travels at 40 kmph. While walking back at 4 kmph, halfway through, he suddenly realized he was getting late and he cycled back the remaining distance in 30 kmph. Find the average speed.

(a) 6.5 kmph

(b)12.0 kmph

(c)28.5 kmph

(d) none of these

2.P, Q and R together earn Rs.1620 in 9 days. P and R can earn Rs.600 in 5 days. Q and R in 7 days can earn Rs.910. How much amount does R can earn per day?

(a) Rs. 20

(b) Rs.30

(c) Rs.70

(d) Rs.40

3.A work can be finished in 16 days by twenty women. The same work can be finished in fifteen days by sixteen men. The ratio between the capacity of a man and a woman is

(a) 2 : 4

(b) 4 : 3

(c) 2 : 3

(d) 3 : 6

4.A completes 80% of a work in 20 days. Then B also joins and A and B together finish the remaining work in 3 days. How long does it need for B if he alone completes the work?

(a) 39 ½ days

(b) 37 ½

(c) 40 days

(d) None of these

5.If 6 men or 12 women can do a piece of work in 32 days, in how many days 48 men and 32 women will do the same piece of work?

(a) 4 days

(b) 8 days

(c) 6 days

(d) 3 days

6.If 50% of (x – y) = 20% of (x + y), then what percent of x is y?

(a) 250/7 %

(b) 300/7 %

(c) 150/7 %

(d) 42%

7.In a school 70% of the students are girls. The number of boys are 510. Then the total number of students in the school is:

(a) 850

(b) 1700

(c) 1830

(d) 2000

8.A merchant has 1000 kg of sugar part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The Quantity sold at 18% profit is

(a) 400

(b) 300

(c) 600

(d) 250

9.Mr. Thomas invested an amount of Rs. 13,900 divided in two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be Rs. 3508, what was the amount invested in Scheme A?

(a) Rs. 6400

(b) Rs. 7200

(c) Rs. 6500

(d) Rs. 7500

10.Rs.460 was divided among 41, boys and girls such that each boy Rs.12 and each girl got Rs.8. What is the number of boys?

(a) 33

(b) 30

(c) 36

(d) 28

Answers and Solution:

1.(b)

2.(c) : Amount Earned by P,Q and R in 1 day = 1620/9 = 180 —(1)

Amount Earned by P and R in 1 day = 600/5 = 120 —(2)

Amount Earned by Q and R in 1 day = 910/7 = 130 —(3)

(2)+(3)-(1) => Amount Earned by P , Q and 2R in 1 day

– Amount Earned by P,Q and R in 1 day = 120+130-180 = 70

=>Amount Earned by R in 1 day = 70

3.(b) : Work done by 20 women in 1 day = 1/16

Work done by 1 woman in 1 day = 1/(16×20)

Work done by 16 men in 1 day = 1/15

Work done by 1 man in 1 day = 1/(15×16)

Ratio of the capacity of a man and woman =1/(15×16) : 1/(16×20) = 1/15 : 1/20

= 1/3 :1/4 = 4:3

4.(b) : Work done by A in 20 days = 80/100 = 8/10 = 4/5

Work done by A in 1 day = (4/5) / 20 = 4/100 = 1/25 — (1)

Work done by A and B in 3 days = 20/100 = 1/5 (Because remaining 20% is done in 3 days by A and B)

Work done by A and B in 1 day = 1/15 —(2)

Work done by B in 1 day = 1/15 – 1/25 = 2/75

=> B can complete the work in 75/2 days = 37 ½ days

5.(d) : 6 men = 12 women ⇒ 1 man = 2 women

48 men = (12/2) x 48 = 96 women

total women = 96 + 32 = 128

12 women can do a piece of work in 32 days

128 women can do a piece of work =(32 x 12)/128 = 3 days

6.(b); 5(x – y) = 2(x + y) ⇒ 5x – 2x = 7y

3x = 7y => y = 3x/7 = (3/7) * 100 = 300/7%

7.(b); % of number of boys = 100 – 70 = 30%

Since 30% = 510, So, 100% = 1700

8.(c)

9.(a) : Let the investment in scheme A be Rs.x

and the investment in scheme B be Rs.(13900 – x)

We know that SI = PRT/100

Simple Interest for Rs.x in 2 years at 14% p.a. = (x*14*2)/100=28x/100

Simple Interest for Rs.(13900 – x) in 2 years at 11% p.a. = [(13900−x) *11*2]/100=22(13900−x)/100

Total interest = Rs.3508

[28x/100]+22(13900−x)/100=3508

28x+305800−22x=350800

6x=45000

x=45000/6=7500

Investment in scheme B = 13900 – 7500 = Rs.6400

10.(a) : Assume that the number of boys = b and number of girls is g

number of boys + number of girls = 41

=> b + g = 41 ———— (Equation 1)

Given that each boy got Rs.12 and each girl got Rs.8 and Total amount = Rs.460

=> 12b + 8g = 460 ——– (Equation 2)

Now we need solve Equation 1 and Equation 2 to get b and g

(Equation1)×8=>8b+8g=8×41=328−−−−−−−−(Equation3)

(Equation 2) – (Equation 3) = 4b = (460 – 328) = 132 => b = 33

**Find solutions for all the questions at the end of each set:**