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Maths Quiz for CTET Exam 2016

1. At present Ayushi is eight times her daughter’s age. Eight years from now, the ratio of the ages of Ayushi and her daughter will be 10 : 3 respectively. What is Ayushi’s present age ?
A. 32 years
B. 40 years
C. 36 years
D. Can’t say
Solution:
Let the age of Ayushi’s daughter be x.
Then Ayushi’s age is 8x. (8x + 8)/ (x + 8) = 10/3 ….x = 4
Ayushi present age = 8x = 32 years.

2. In how many different ways can 4 boys and 3 girls be arranged in a row such that all the boys stand together and all the girls stand together?
A. 75
B. 576
C. 288
D. 24
Solution:
Required number of ways = 4! * 3! * 2! = 288.

3. A radio is sold for Rs 990 at a profit of 10%. What would have been the gain or loss in percentage had it been sold for Rs 880?
A. 19/3% gain
B. 17/3% loss
C. 17% gain
D. 20/9% loss
Solution:
Let the CP is Rs x.
Then, x * 110/100 = 990 x = 900
Now CP is Rs 900 and SP is 880.
% loss = 20/900 * 100 = 20/9%

4.The population of a city is 1500000. It increases by 10% during 1st yr, decreases by 20% in 2nd yr and increases by 30% in the 3rd yr. The population after 3 years ?
A. 1716000
B. 1750000
C. 1650000
D. 1600000
Solution:
Initial population = 15,00000;
After first year increment of 10 %, population = 1500000 + 10/100 × 1500000 = 1650000
After second year decrement of 20%, population = 1650000 – 20/100 × 1650000 = 1320000
After increment of 30 % in third year = 1320000 + 30/100 × 1320000 = 1716000

5. A, B and C undertake to complete a piece of work for Rs 1950. A works for 8 days, B for 9 days and C for 12 days to complete the work. If their daily wages are in the ratio of 3 : 5 : 4, how much C get?
A. 400
B. 750
C. 675
D. 800
Solution:
Daily wages are in the ratio 3 : 5 : 4 ,
working days of A,B,C = 8,9 and 12
so the wages they get will be in ratio 24 : 45 : 48,
Share of C = 48/(24+45+48) × 1950 = Rs 800

6. A horse and a cow were sold for Rs. 12,000 each. This gave a loss of 20% on horse and a gain of 20% on cow. The entire transaction resulted in
A. no loss no gain
B. loss of Rs. 1,000
C. gain of Rs. 10,000
D. loss of Rs. 100
Solution:
Loss of 20% on one and gain of 20% on other.
⇒ there will be a loss (always)
and loss% = (20)^2/100% = 4%loss (on total C.P.)
⇒ C.P. (100%)    –4%_  S.P. (96%)
= 12,000 × 2 = 24000
So, loss in transaction (i.e. 4%)
= 24000 × 4/96 = 1000
⇒ loss of Rs. 1000

7. When an article is sold for Rs. 116, the profit percent is thrice as much as when it is sold for Rs. 92. The cost price of the article is
A. Rs. 68
B. Rs. 72
C. Rs. 78
D. Rs. 80
Solution:
116 – 92 = 24         Let x = profit when S.P. = 92
i.e. 3x – x = 24 So, 3x = profit when S.P. = 116
⇒ x = 12
⇒ When S.P. = 92, Profit = Rs. 12
So, C.P. = 92 – 12 = Rs. 80

8. If the total cost of 73 articles having equal cost is Rs. 5,110 and the total selling price of 89 such articles if Rs. 5,607, then in the transaction, there will be
A. a loss of 15%
B. a gain of 10%
C. a loss of 10%
D. a gain of 15%
Solution:
C.P. of each article = Rs. 5110/73 = Rs. 70
S.P. of each article = Rs. 5607/89 = Rs. 63
Here, S.P. < C.P. ⇒ loss
and % loss = (S.P. – C.P.) × 100% /C.P.
= (63 – 70) × 100%/70
= – 10%
= 10% loss

9. By selling an articles for Rs. 665, there is a loss of 5%. In order to make a profit of 12%, the selling price of the article must be
A. Rs. 812
B. Rs. 800
C. Rs. 790
D. Rs. 784
Solution:
C.P. (100%)    –5%    S.P. (95%) = Rs. 665
S.P. at 5% loss i.e. 95% of C.P. = Rs. 665
So, SP at 12% profit i.e. 112% of C.P.
= Rs. 665 × 112/95= Rs. 784

10. Nitin’s salary was reduced by 10% and then the reduced salary was increased by 10%. His new salary in comparison with his original salary is
A. the same
B. 1% more
C. 1% less
D. 5% less
Solution:
Less by ((10)^2/100)% = i.e. less by 1% Join India's largest learning destination

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