1. Amina thinks of a number and subtracts from it. She multiplies the result by 8. The result now obtained is 3 times the same number she thought of. What is the number?
2. A positive number is 5 times another number. If 21 is added to both the numbers, then one of the new numbers becomes twice the other new number. What are the numbers?
3. Sum of the digits of a two-digit number is 9. When we interchange the digits, it is found that the resulting new number is greater than the original number by 27. What is the two-digit number?
4. One of the two digits of a two digit number is three times the other digit. If you interchange the digits of this two-digit number and add the resulting number to the original number, you get 88. What is the original number? 5. Shobo's mother's present age is six times Shobo's present age. Shobo's age five years from now will be one third of his mother's present age. What are their present ages?
6. There is a narrow rectangular plot, reserved for a school, in Mahuli village. The length and breadth of the plot are in the ratio 11:4. At the rate ₹100 per metre it will cost the village panchayat ₹75000 to fence the plot. What are the dimensions of the plot?
7. Hasan buys two kinds of cloth materials for school uniforms, shirt material that costs him ₹50 per metre and trouser material that costs him ₹90 per metre.
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Answer:
Let Amina think a number x.
According to the question, 8\left(x-\frac{5}{2}\right)=3x8(x−
2
5
)=3x
\Rightarrow\ 8x-\frac{8\times5}{2}=3x⇒ 8x−
2
8×5
=3x
\Rightarrow\ 8x-4\times5=3x⇒ 8x−4×5=3x
\Rightarrow8x-20=3x⇒8x−20=3x
\Rightarrow8x-3x=20⇒8x−3x=20
\Rightarrow5x=20⇒5x=20
\Rightarrow x=\frac{20}{5}=4⇒x=
5
20
=4
Hence, the number is
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