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Q:

An intelligent boy is doing a jigsaw with 275 pieces. Each day that he fits pieces together there are fewer pieces left, and it is reasonable to assume that he fits more pieces each day because the number left to sort out diminishes progressively. Hence he is able to fit an extra piece as each day goes by. On the first day he fits 20 pieces. How many days does it take for him to complete the puzzle ?

A) 11 days	B) 15 days
C) 13 days	D) 16 days

Answer & Explanation Answer: A) 11 days

Explanation:

Let 'n' number of days it take to complete.

we know that sum of n number= n/2[2a+(n-1)d]
where a=20,d=1;
n/2[2x20+(n-1)1]=275
n[n+39]=550
$n^{2}$ + 39n - 550 = 0
$n^{2}$ + 50n - 11n - 550 = 0
(n-11) (n-50) = 0
n-11 = 0;
n = 11(Days).

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Q:

If the true discount on s sum due 2 years hence at 14% per annum be Rs. 168, the sum due is ?

A) Rs.948	B) Rs.876
C) Rs.768	D) Rs.658

Answer & Explanation Answer: C) Rs.768

Explanation:

P.W. = $\frac{100 \times T . D}{R \times T}$ = $\frac{100 \times 168}{14 \times 2}$ = 600.

Sum = (P.W. + T.D.) = Rs. (600 + 168) = Rs. 768.

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Q:

The ratio of present ages of Hema and Chinnu is 13:17. Four years ago the ratio of their ages was 11:15. What will be the ratio of their ages six years hence ?

A) 3 : 7	B) 7 : 9
C) 4 : 5	D) 1 : 3

Answer & Explanation Answer: C) 4 : 5

Explanation:

Let their present ages be 13x and 17x.
Then, 13x-4/17x-4 = 11/15.
Solving this, we get x = 2.
Required ratio = 13x2 + 6/17x2 + 6 = 32/40 = 4/5.

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Q:

5 years ago Sushma was 5 times as old as her Son. 5 years hence her age will be 8 less than three times the corresponding age of her Son. Find their ages ?

A) 24 and 13 years	B) 48 and 24 years
C) 35 and 11 years	D) 33 and 15 years

Answer & Explanation Answer: C) 35 and 11 years

Explanation:

Let the age of sushma be x and
the age of her son is y
Then five years before x-5=5(y-5) ...(1)
Five years hence x+5 = 3(y+5)-8 .....(2)

By soving (1) & (2), we get
5y - 15 = 3y + 7
y = 11 => x = 35

Therefore, the age of Sushma = 35 and her son = 11.

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Q:

The market price of an article was 40% more than its cost price. Rana was going to sell it at market price to a customer, but he showed Rana some defects in the article, due to which Rana gave him a discount of 28.57%. Next day he came again and showed Rana some more defects, hence he gave him another discount that was equal to 12.5% of the cost price. What was the approximate profit/loss to Rana ?

A) Loss of 12.5%	B) Profit of 12.5%
C) Loss of 24.5%	D) Profit of 22.5%

Answer & Explanation Answer: A) Loss of 12.5%

Explanation:

Let the cost price be Rs. 100
Then, market price is Rs. 140
Now, the first discount is of 28.57% Rs.140 =~ Rs. 40
Hence, its selling price = 140 - 40 = Rs. 100
Now since Rana is selling at cost price, any further discount will be equal to loss percentage.
The next dicount of 12.5% will be the loss percentage to Rana.

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Q:

Ten years ago, Karan was thrice as old as Shiva was but 10 years hence, he will be only twice as old. Find Shiva’s present age ?

A) 70 years	B) 30 years
C) 60 years	D) 40 years

Answer & Explanation Answer: B) 30 years

Explanation:

Let Karan’s present age be x years and Shiva’s present age be y years.
Then, according to the first condition,
x - 10 = 3(y - 10) or x - 3y = - 20 ..(1)
Now, Karan’s age after 10 years = (x + 10) years
Shiva’s age after 10 years = (y + 10)
(x + 10) = 2 (y + 10) or x - 2y = 10 ..(2)
Solving (1) and (2), we get x = 70 and y = 30
Karan’s age = 70 years and Shiva’s age = 30 years.

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Q:

The ratio of Karthik’s and Kalyan’s ages is 4: 5. If the difference between the present age of Kalyan and the age of Karthik 5 years hence is 3 years, then what is the total of present ages of Karthik and Kalyan?

A) 56 years	B) 62 years
C) 69 years	D) 72 years

Answer & Explanation Answer: D) 72 years

Explanation:

Let us consider Karthik as K1 and Kalyan as K2.

Given $\frac{k 1}{8 + k 1}$ and K2 - (K1 + 5) = 3

K2 - K1 = 8

K2 = 8 + K1

Now,

$\frac{k 1}{8 + k 1} = \frac{4}{5}$

=> K1 = 32 years

Therefore K2 = 40 years.

K1 + K2 = 72 years.

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Q:

Ten years ago, Kumar was thrice as old as Sailesh was but 10 years hence, he will be only twice as old. Find Kumar’s present age ?

A) 50 years	B) 70 years
C) 60 years	D) 40 years

Answer & Explanation Answer: B) 70 years

Explanation:

Let Kumar’s present age be "x" years and Sailesh’s present age be "y" years.
Then, according to the first condition,

x - 10 = 3(y - 10) => x - 3y = - 20 ........(1)

Now, Kumar’s age after 10 years = (x + 10) years.

Sailesh’s age after 10 years = (y + 10) years.

(x + 10) = 2 (y + 10) => x - 2y = 10 ......(2)

Solving (1) and (2),

we get x = 70 and y = 30

Kumar’s present age = 70 years and Sailesh’s present age = 30 years.

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Filed Under: Problems on Ages
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